| 1. |
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| 2. |
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| 3. |
- Alekseev, Victor, et al.
(författare)
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Localizing non-linear N = (2,2) sigma model on S-2
- 2022
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Ingår i: European Physical Journal C. - : Springer. - 1434-6044 .- 1434-6052. ; 82:8
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Tidskriftsartikel (refereegranskat)abstract
- We present a systematic study of N = (2, 2) supersymmetric non-linear sigma models on S-2 with the target being a Kahler manifold. We discuss their reformulation in terms of cohomological field theory. In the cohomological formulation we use a novel version of 2D self-duality which involves a U(1) action on S-2. In addition to the generic model we discuss the theory with target space equivariance corresponding to a supersymmetric sigmamodel coupled to a non-dynamical supersymmetric background gauge multiplet. We discuss the localization locus and perform a one-loop calculation around the constant maps. We argue that the theory can be reduced to some exotic model over the moduli space of holomorphic disks.
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| 4. |
- Bischoff, Francis, et al.
(författare)
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Morita equivalence and the generalized Kähler potential
- 2022
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Ingår i: Journal of differential geometry. - : International Press of Boston. - 0022-040X .- 1945-743X. ; 121:2, s. 187-226
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Tidskriftsartikel (refereegranskat)abstract
- We solve the problem of determining the fundamental degrees of freedom underlying a generalized Kahler structure of symplectic type. For a usual Kahler structure, it is well-known that the geometry is determined by a complex structure, a Kahler class, and the choice of a positive (1, 1)-form in this class, which depends locally on only a single real-valued function: the Kahler potential. Such a description for generalized Kahler geometry has been sought since it was discovered in 1984. We show that a generalized Kahler structure of symplectic type is determined by a pair of holomorphic Poisson manifolds, a holomorphic symplectic Morita equivalence between them, and the choice of a positive Lagrangian brane bisection, which depends locally on only a single real-valued function, which we call the generalized Kahler potential. Our solution draws upon, and specializes to, the many results in the physics literature which solve the problem under the assumption (which we do not make) that the Poisson structures involved have constant rank. To solve the problem we make use of, and generalize, two main tools: the first is the notion of symplectic Morita equivalence, developed by Weinstein and Xu to study Poisson manifolds; the second is Donaldson's interpretation of a Kahler metric as a real Lagrangian submanifold in a deformation of the holomorphic cotangent bundle.
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| 5. |
- Bonechi, Francesco, et al.
(författare)
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AKSZ construction from reduction data
- 2012
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Ingår i: Journal of High Energy Physics (JHEP). - : Springer. - 1126-6708 .- 1029-8479. ; :7
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Tidskriftsartikel (refereegranskat)abstract
- We discuss a general procedure to encode the reduction of the target space geometry into AKSZ sigma models. This is done by considering the AKSZ construction with target the BFV model for constrained graded symplectic manifolds. We investigate the relation between this sigma model and the one with the reduced structure. We also discuss several examples in dimension two and three when the symmetries come from Lie group actions and systematically recover models already proposed in the literature.
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| 6. |
- Bonechi, F., et al.
(författare)
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Equivariant Batalin-Vilkovisky formalism
- 2020
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Ingår i: Journal of Geometry and Physics. - : ELSEVIER. - 0393-0440 .- 1879-1662. ; 154
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Tidskriftsartikel (refereegranskat)abstract
- We study an equivariant extension of the Batalin-Vilkovisky formalism for quantizing gauge theories. Namely, we introduce a general framework to encompass failures of the quantum master equation, and we apply it to the natural equivariant extension of AKSZ solutions of the classical master equation (CME). As examples of the construction, we recover the equivariant extension of supersymmetric Yang-Mills in 2d and of Donaldson-Witten theory. (C) 2020 Elsevier B.V. All rights reserved.
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| 7. |
- Bonechi, Francesco, et al.
(författare)
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Finite-Dimensional AKSZ-BV Theories
- 2010
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Ingår i: Letters in Mathematical Physics. - : Springer Science and Business Media LLC. - 0377-9017 .- 1573-0530. ; 94:2, s. 197-228
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Tidskriftsartikel (refereegranskat)abstract
- We describe a canonical reduction of AKSZ-BV theories to the cohomology of the source manifold. We get a finite-dimensional BV theory that describes the contribution of the zero modes to the full QFT. Integration can be defined and correlators can be computed. As an illustration of the general construction, we consider two-dimensional Poisson sigma model and three-dimensional Courant sigma model. When the source manifold is compact, the reduced theory is a generalization of the AKSZ construction where we take as source the cohomology ring. We present the possible generalizations of the AKSZ theory.
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| 8. |
- Bonechi, Francesco, et al.
(författare)
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Lie algebroids, Lie groupoids and TFT
- 2007
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Ingår i: Journal of Geometry and Physics. - : Elsevier BV. - 0393-0440 .- 1879-1662. ; 57:3, s. 731-744
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Tidskriftsartikel (refereegranskat)abstract
- We construct the moduli spaces associated to the solutions of equations of motion (modulo gauge transformations) of the Poisson sigma model with target being an integrable Poisson manifold. The construction can be easily extended to a case of a generic integrable Lie algebroid. Indeed for any Lie algebroid one can associate a BF-like topological field theory which localizes on the space of algebroid morphisms, that can be seen as a generalization of flat connections to the groupoid case. We discuss the finite gauge transformations and discuss the corresponding moduli spaces. We consider the theories both without and with boundaries.
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| 9. |
- Bonechi, F., et al.
(författare)
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Observables in the equivariant A-model
- 2020
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Ingår i: Letters in Mathematical Physics. - : Springer Nature. - 0377-9017 .- 1573-0530. ; 110:4, s. 695-711
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Tidskriftsartikel (refereegranskat)abstract
- We discuss observables of an equivariant extension of the A-model in the framework of the AKSZ construction. We introduce the A-model observables, a class of observables that are homotopically equivalent to the canonical AKSZ observables but are better behaved in the gauge fixing. We discuss them for two different choices of gauge fixing: The first one is conjectured to compute the correlators of the A-model which target the Marsden–Weinstein reduced space; in the second one we recover the topological Yang–Mills action coupled with A-model so that the A-model observables are closed under supersymmetry.
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| 10. |
- Bonechi, Francesco, et al.
(författare)
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Poisson Sigma Model on the Sphere
- 2009
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Ingår i: Communications in Mathematical Physics. - : Springer Science and Business Media LLC. - 0010-3616 .- 1432-0916. ; 285:3, s. 1033-1063
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Tidskriftsartikel (refereegranskat)abstract
- We evaluate the path integral of the Poisson sigma model on the sphere and study the correlators of quantum observables. We argue that for the path integral to be well-defined the corresponding Poisson structure should be unimodular. The construction of the finite dimensional BV theory is presented and we argue that it is responsible for the leading semiclassical contribution. For a (twisted) generalized Kahler manifold we discuss the gauge fixed action for the Poisson sigma model. Using the localization we prove that for the holomorphic Poisson structure the semiclassical result for the correlators is indeed the full quantum result.
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| 11. |
- Bonechi, F., et al.
(författare)
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Towards equivariant Yang-Mills theory
- 2023
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Ingår i: Journal of Geometry and Physics. - : Elsevier. - 0393-0440 .- 1879-1662. ; 189
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Tidskriftsartikel (refereegranskat)abstract
- We study four dimensional gauge theories in the context of an equivariant extension of the Batalin-Vilkovisky (BV) formalism. We discuss the embedding of BV Yang-Mills (YM) theory into a larger BV theory and their relation. Partial integration in the equivariant BV setting (BV push-forward map) is performed explicitly for the abelian case. As result, we obtain a non-local homological generalization of the Cartan calculus and a non-local extension of the abelian YM BV action which satisfies the equivariant master equation.
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| 12. |
- Bonechi, Francesco, et al.
(författare)
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Wilson Lines from Representations of NQ-Manifolds
- 2014
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Ingår i: International mathematics research notices. - : Oxford University Press (OUP). - 1073-7928 .- 1687-0247. ; :9, s. 2440-2493
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Tidskriftsartikel (refereegranskat)abstract
- An NQ-manifold is a non-negatively graded supermanifold with a degree 1 homological vector field. The focus of this paper is to define the Wilson loops/lines in the context of NQ-manifolds and to study their properties. The Wilson loops/lines, which give the holonomy or parallel transport, are familiar objects in usual differential geometry, we analyze the subtleties in the generalization to the NQ-setting and we also sketch some possible applications of our construction.
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| 13. |
- Bonelli, Giulio, et al.
(författare)
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On topological M-theory
- 2006
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Ingår i: Advances in Theoretical and Mathematical Physics. - 1095-0761 .- 1095-0753. ; 10:2, s. 239-260
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Tidskriftsartikel (refereegranskat)abstract
- We construct a gauge-fixed action for topological membranes on G2-manifolds such that its bosonic part is the standard membrane theory in a particular gauge. We prove that the path integral in this gauge localizes on associative submanifolds. Moreover on M × S1, the theory naturally reduces to the standard A-model on Calabi-Yau manifold and to a membrane theory localized on special Lagrangian submanifolds. We discuss some properties of topological membrane theory on G2-manifolds. We also generalize our construction to topological p-branes on special manifolds by exploring a relation between vector cross product structures and TFTs.
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| 14. |
- Bonelli, Giulio, et al.
(författare)
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Topological branes, p-algebras and generalized Nahm equations
- 2009
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Ingår i: Physics Letters B. - : Elsevier BV. - 0370-2693 .- 1873-2445. ; 672:4-5, s. 390-395
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Tidskriftsartikel (refereegranskat)abstract
- Inspired by the recent advances in multiple M2-brane theory, we consider the generalizations of Nahm equations for arbitrary p-algebras. We construct the topological p-algebra quantum mechanics associated to them and we show that this can be obtained as a truncation of the topological p-brane theory previously studied by the authors. The resulting topological p-algebra quantum mechanics is discussed in detail and the relation with the M2-M5 system is pointed out in the p = 3 case, providing a geometrical argument for the emergence of the 3-algebra structure in the Bagger-Lambert-Gustavsson theory.
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| 15. |
- Bredthauer, Andreas, et al.
(författare)
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Generalized Kähler geometry from supersymmetric sigma models
- 2006
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Ingår i: Letters in Mathematical Physics. - : Springer Science and Business Media LLC. - 0377-9017 .- 1573-0530. ; 77:3, s. 291-308
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Tidskriftsartikel (refereegranskat)abstract
- We give a physical derivation of generalized Kahler geometry. Starting from a supersymmetric nonlinear sigma model, we rederive and explain the results of Gualtieri (Generalized complex geometry, DPhil thesis, Oxford University, 2004) regarding the equivalence between generalized Kahler geometry and the bi-hermitean geometry of Gates et al. (Nucl Phys B248:157, 1984). When cast in the language of supersymmetric sigma models, this relation maps precisely to that between the Lagrangian and the Hamiltonian formalisms. We also discuss topological twist in this context.
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| 16. |
- Cassia, Luca, et al.
(författare)
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Exact SUSY Wilson loops on S-3 from q-Virasoro constraints
- 2019
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Ingår i: Journal of High Energy Physics (JHEP). - : SPRINGER. - 1126-6708 .- 1029-8479. ; :12
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Tidskriftsartikel (refereegranskat)abstract
- Using the ideas from the BPS/CFT correspondence, we give an explicit recur- sive formula for computing supersymmetric Wilson loop averages in 3d N = 2 Yang-Mills-Chern-Simons U(N) theory on the squashed sphere Sb3 with one adjoint chiral and two antichiral fundamental multiplets, for specific values of Chern-Simons level kappa(2) and Fayet- Illiopoulos parameter kappa(1). For these values of kappa(1) and kappa(2) the north and south pole turn out to be completely independent, and therefore Wilson loop averages factorize into answers for the two constituent D(2)x S-1 theories. In particular, our formula provides results for the theory on the round sphere when the squashing is removed.
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| 17. |
- Cassia, Luca, et al.
(författare)
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From equivariant volumes to equivariant periods
- 2023
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Ingår i: Advances in Theoretical and Mathematical Physics. - : International Press. - 1095-0761 .- 1095-0753. ; 27:4, s. 961-1064
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Tidskriftsartikel (refereegranskat)abstract
- We consider generalizations of equivariant volumes of abelian GIT quotients obtained as partition functions of 1d, 2d, and 3d sudefine these objects and study their dependence on equivariant parameters for non-compact toric Kahler quotients. We generalize the finite-difference equations (shift equations) obeyed by equivariant volumes to these partition functions. The partition functions are annihilated by differential/difference operators that represent equivariant quantum cohomology/K-theory relations of the target and the appearance of compact divisors in these relations plays a crucial role in the analysis of the non-equivariant limit. We show that the expansion in equivariant parameters contains information about genus-zero Gromov-Witten invariants of the target.
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| 18. |
- Cassia, Luca, et al.
(författare)
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On matrix models and their q-deformations
- 2020
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Ingår i: Journal of High Energy Physics (JHEP). - : SPRINGER. - 1126-6708 .- 1029-8479. ; :10
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Tidskriftsartikel (refereegranskat)abstract
- Motivated by the BPS/CFT correspondence, we explore the similarities be- tween the classical beta -deformed Hermitean matrix model and the q-deformed matrix models associated to 3d N = 2 supersymmetric gauge theories on D(2)x(q)S(1) and Sb3 by matching parameters of the theories. The novel results that we obtain are the correlators for the models, together with an additional result in the classical case consisting of the W -algebra representation of the generating function. Furthermore, we also obtain surprisingly simple expressions for the expectation values of characters which generalize previously known results.
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| 19. |
- Cassia, Luca, et al.
(författare)
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On refined Chern-Simons and refined ABJ matrix models
- 2022
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Ingår i: Letters in Mathematical Physics. - : Springer Nature. - 0377-9017 .- 1573-0530. ; 112
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Tidskriftsartikel (refereegranskat)abstract
- We consider the matrix model of U(N) refined Chern-Simons theory on S-3 for the unknot. We derive a q-difference operator whose insertion in the matrix integral reproduces an infinite set of Ward identities which we interpret as q-Virasoro constraints. The constraints are rewritten as difference equations for the generating function of Wilson loop expectation values which we solve as a recursion for the correlators of the model. The solution is repackaged in the form of superintegrability formulas for Macdonald polynomials. Additionally, we derive an equivalent q-difference operator for a similar refinement of ABJ theory and show that the corresponding q-Virasoro constraints are equal to those of refined Chern-Simons for a gauge super-group U(N vertical bar M). Our equations and solutions are manifestly symmetric under Langlands duality q <-> t(-1) which correctly reproduces 3d Seiberg duality when q is a specific root of unity.
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| 20. |
- Cassia, Luca, et al.
(författare)
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Virasoro constraints revisited
- 2021
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Ingår i: Communications in Mathematical Physics. - : Springer Nature. - 0010-3616 .- 1432-0916. ; 387:3, s. 1729-1755
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Tidskriftsartikel (refereegranskat)abstract
- We revisit the Virasoro constraints and explore the relation to the Hirota bilinear equations. We furthermore investigate and provide the solution to non-homogeneous Virasoro constraints, namely those coming from matrix models whose domain of integration has boundaries. In particular, we provide the example of Hermitean matrices with positive eigenvalues in which case one can find a solution by induction on the rank of the matrix model.
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| 21. |
- Cassia, Luca, et al.
(författare)
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β-Ensembles and higher genera Catalan numbers
- 2024
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Ingår i: Letters in Mathematical Physics. - : Springer. - 0377-9017 .- 1573-0530. ; 114:1
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Tidskriftsartikel (refereegranskat)abstract
- We propose formulas for the large N expansion of the generating function of connected correlators of the β-deformed Gaussian and Wishart–Laguerre matrix models. We show that our proposal satisfies the known transformation properties under the exchange of β with 1 / β and, using Virasoro constraints, we derive a recursion formula for the coefficients of the expansion. In the undeformed limit β = 1, these coefficients are integers and they have the combinatorial interpretation of generalized Catalan numbers. For generic β, we define the higher genus Catalan polynomials Cg,v(β) whose coefficients are integer numbers.
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| 22. |
- Cattaneo, Alberto S., et al.
(författare)
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2D and 3D topological field theories for generalized complex geometry
- 2010
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Ingår i: Advances in Theoretical and Mathematical Physics. - 1095-0761 .- 1095-0753. ; 14:2, s. 695-725
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Tidskriftsartikel (refereegranskat)abstract
- Using the Alexandrov-Kontsevich-Schwarz-Zaboronsky (AKSZ) prescription we construct 2D and 3D topological field theories associated to generalized complex manifolds. These models can be thought of as 2D and 3D generalizations of A-and B-models. Within the BV framework we show that the 3D model on a two-manifold cross an interval can be reduced to the 2D model.
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| 23. |
- Del Zotto, Michele, et al.
(författare)
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Playing With the Index of M-Theory
- 2022
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Ingår i: Communications in Mathematical Physics. - : Springer Nature. - 0010-3616 .- 1432-0916. ; 396:2, s. 817-865
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Tidskriftsartikel (refereegranskat)abstract
- Motivated by M-theory, we study rank n K-theoretic Donaldson-Thomas theory on a toric threefold X. In the presence of compact four-cycles, we discuss how to include the contribution of D4-branes wrapping them. Combining this with a simple assumption on the (in)dependence on Coulomb moduli in the 7d theory, we show that the partition function factorizes and, when X is Calabi-Yau and it admits an ADE ruling, it reproduces the 5d master formula for the geometrically engineered theory on A(n-1) ALE space, thus extending the usual geometric engineering dictionary to n > 1. We finally speculate about implications for instanton counting on Taub-NUT.
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| 24. |
- Ekstrand, Joel, et al.
(författare)
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Chiral de Rham complex on Riemannian manifolds and special holonomy
- 2013
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Ingår i: Communications in Mathematical Physics. - : Springer Science and Business Media LLC. - 0010-3616 .- 1432-0916. ; 318:3, s. 575-613
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Tidskriftsartikel (refereegranskat)abstract
- Interpreting the chiral de Rham complex (CDR) as a formal Hamiltonian quantization of the supersymmetric non-linear sigma model, we suggest a setup for the study of CDR on manifolds with special holonomy. We discuss classical and partial quantum results. As a concrete example, we construct two commuting copies of the Odake algebra (an extension of the N=2 superconformal algebra) on the space of global sections of CDR of a Calabi-Yau 3-fold. This is the first example of such a vertex subalgebra which is non-linearly generated by a finite number of superfields.
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| 25. |
- Ekstrand, Joel, et al.
(författare)
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Courant-like brackets and loop spaces
- 2011
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Ingår i: Journal of High Energy Physics (JHEP). - 1126-6708 .- 1029-8479. ; 2011:3, s. 074-
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Tidskriftsartikel (refereegranskat)abstract
- We study the algebra of local functionals equipped with a Poisson bracket. We discuss the underlying algebraic structures related to a version of the Courant-Dorfman algebra. As a main illustration, we consider the functionals over the cotangent bundle of the superloop space over a smooth manifold. We present a number of examples of the Courant-like brackets arising from this analysis.
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| 26. |
- Ekstrand, Joel
(författare)
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Going Round in Circles : From Sigma Models to Vertex Algebras and Back
- 2011
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- In this thesis, we investigate sigma models and algebraic structures emerging from a Hamiltonian description of their dynamics, both in a classical and in a quantum setup. More specifically, we derive the phase space structures together with the Hamiltonians for the bosonic two-dimensional non-linear sigma model, and also for the N=1 and N=2 supersymmetric models. A convenient framework for describing these structures are Lie conformal algebras and Poisson vertex algebras. We review these concepts, and show that a Lie conformal algebra gives a weak Courant–Dorfman algebra. We further show that a Poisson vertex algebra generated by fields of conformal weight one and zero are in a one-to-one relationship with Courant–Dorfman algebras. Vertex algebras are shown to be appropriate for describing the quantum dynamics of supersymmetric sigma models. We give two definitions of a vertex algebra, and we show that these definitions are equivalent. The second definition is given in terms of a λ-bracket and a normal ordered product, which makes computations straightforward. We also review the manifestly supersymmetric N=1 SUSY vertex algebra. We also construct sheaves of N=1 and N=2 vertex algebras. We are specifically interested in the sheaf of N=1 vertex algebras referred to as the chiral de Rham complex. We argue that this sheaf can be interpreted as a formal quantization of the N=1 supersymmetric non-linear sigma model. We review different algebras of the chiral de Rham complex that one can associate to different manifolds. In particular, we investigate the case when the manifold is a six-dimensional Calabi–Yau manifold. The chiral de Rham complex then carries two commuting copies of the N=2 superconformal algebra with central charge c=9, as well as the Odake algebra, associated to the holomorphic volume form.
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| 27. |
- Ekstrand, Joel, et al.
(författare)
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Non-linear sigma models via the chiral de Rham complex
- 2009
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Ingår i: Advances in Theoretical and Mathematical Physics. - 1095-0761 .- 1095-0753. ; 13:4, s. 1221-1254
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Tidskriftsartikel (refereegranskat)abstract
- We propose a physical interpretation of the chiral de Rham complex as a formal Hamiltonian quantization of the supersymmetric non-linear sigma model. We show that the chiral de Rham complex on a Calabi-Yau manifold carries all information about the classical dynamics of the sigma model. Physically, this provides an opera- tor realization of the non-linear sigma model. Mathematically, the idea suggests the use of Hamiltonian flow equations within the vertex algebra formalism with the pos- sibility to incorporate both left and right moving sectors within one mathematical framework.
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| 28. |
- Ekstrand, Joel, et al.
(författare)
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Sheaves of N=2 supersymmetric vertex algebras on Poisson manifolds
- 2012
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Ingår i: Journal of Geometry and Physics. - : Elsevier BV. - 0393-0440 .- 1879-1662. ; 62:11, s. 2259-2278
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Tidskriftsartikel (refereegranskat)abstract
- We construct a sheaf of N = 2 vertex algebras naturally associated to any Poisson manifold. The relation of this sheaf to the chiral de Rham complex is discussed. We reprove the result about the existence of two commuting N = 2 superconformal structures on the space of sections of the chiral de Rham complex of a Calabi-Yau manifold, but now calculated in a manifest N = 2 formalism. We discuss how the semi-classical limit of this sheaf of N = 2 vertex algebras is related to the classical supersymmetric non-linear sigma model.
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| 29. |
- Festuccia, Guido, et al.
(författare)
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N=2 supersymmetric gauge theory on connected sums of S2xS2
- 2017
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Ingår i: Journal of High Energy Physics (JHEP). - 1126-6708 .- 1029-8479. ; 03
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Tidskriftsartikel (refereegranskat)abstract
- We construct 4D N = 2 theories on an infinite family of 4D toric manifolds with the topology of connected sums of S-2 x S-2. These theories are constructed through the dimensional reduction along a non -trivial U(1) -fiber of 5D theories on toric Sasaki Einstein manifolds. We discuss the conditions under which such reductions can be carried out and give a partial classification result of the resulting 4D manifolds. We calculate the partition functions of these 4D theories and they involve both instanton and anti-instanton contributions, thus generalizing Pestun's famous result on S-4.
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| 30. |
- Festuccia, Guido, et al.
(författare)
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S-duality and supersymmetry on curved manifolds
- 2020
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Ingår i: Journal of High Energy Physics (JHEP). - 1126-6708 .- 1029-8479. ; :9
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Tidskriftsartikel (refereegranskat)abstract
- We perform a systematic study of S-duality for N = 2 supersymmetric non-linear abelian theories on a curved manifold. Localization can be used to compute certain supersymmetric observables in these theories. We point out that localization and S-duality acting as a Legendre transform are not compatible. For these theories S-duality should be interpreted as Fourier transform and we provide some evidence for this. We also suggest the notion of a coholomological prepotential for an abelian theory that gives the same partition function as a given non-abelian supersymmetric theory.
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| 31. |
- Festuccia, Guido, et al.
(författare)
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Transversally elliptic complex and cohomological field theory
- 2020
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Ingår i: Journal of Geometry and Physics. - : ELSEVIER. - 0393-0440 .- 1879-1662. ; 156, s. 103786-
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Tidskriftsartikel (refereegranskat)abstract
- This work is a continuation of our previous paper arXiv: 1812.06473 where we have constructed N = 2 supersymmetric Yang-Mills theory on 4D manifolds with a Killing vector field with isolated fixed points. In this work we expand on the mathematical aspects of the theory, with a particular focus on its nature as a cohomological field theory. The well-known Donaldson-Witten theory is a twisted version of N = 2 SYM and can also be constructed using the Atiyah-Jeffrey construction (Atiyah and Jeffrey, 1990). This theory is concerned with the moduli space of anti-self-dual gauge connections, with a deformation theory controlled by an elliptic complex. More generally, supersymmetry requires considering configurations that look like either instantons or anti-instantons around fixed points, which we call flipping instantons. The flipping instantons of our 4D N = 2 theory are derived from the 5D contact instantons. The novelty is that their deformation theory is controlled by a transversally elliptic complex, which we demonstrate here. We repeat the Atiyah-Jeffrey construction in the equivariant setting and arrive at the Lagrangian (an equivariant Euler class in the relevant field space) that was also obtained from our previous work arXiv: 1812.06473. We show that the transversal ellipticity of the deformation complex is crucial for the non-degeneracy of the Lagrangian and the calculability of the theory. Our construction is valid on a large class of quasi toric 4 manifolds. (C) 2020 Elsevier B.V. All rights reserved.
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| 32. |
- Festuccia, Guido, et al.
(författare)
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Twisting with a Flip (The Art of Pestunization)
- 2020
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Ingår i: Communications in Mathematical Physics. - : SPRINGER. - 0010-3616 .- 1432-0916. ; 377:1, s. 341-385
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Tidskriftsartikel (refereegranskat)abstract
- We construct N=2supersymmetric Yang-Mills theory on 4D manifolds with a Killing vector field with isolated fixed points. It turns out that for every fixed point one can allocate either instanton or anti-instanton contributions to the partition function, and that this is compatible with supersymmetry. The equivariant Donaldson-Witten theory is a special case of our construction. We present a unified treatment of Pestun's calculation on S4\ and equivariant Donaldson-Witten theory by generalizing the notion of self-duality on manifolds with a vector field. We conjecture the full partition function for a N=2 theory on any 4D manifold with a Killing vector. Using this new notion of self-duality to localize a supersymmetric theory is what we call "Pestunization".
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| 33. |
- Heluani, Reimundo, et al.
(författare)
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Generalized Calabi-Yau manifolds and the chiral de Rham complex
- 2010
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Ingår i: Advances in Mathematics. - : Elsevier BV. - 0001-8708 .- 1090-2082. ; 223:5, s. 1815-1844
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Tidskriftsartikel (refereegranskat)abstract
- We show that the chiral de Rham complex of a generalized Calabi-Yau manifold carries N = 2 supersymmetry. We discuss the corresponding topological twist for this N = 2 algebra. We interpret this as an algeboid version of the super-Sugawara or Kac-Todorov construction.
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| 34. |
- Heluani, Reimundo, et al.
(författare)
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Superconformal Structures on Generalized Calabi-Yau Metric Manifolds
- 2011
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Ingår i: Communications in Mathematical Physics. - : Springer Science and Business Media LLC. - 0010-3616 .- 1432-0916. ; 306:2, s. 333-364
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Tidskriftsartikel (refereegranskat)abstract
- We construct an embedding of two commuting copies of the N = 2 superconformal vertex algebra in the space of global sections of the twisted chiral-anti-chiral de Rham complex of a generalized Calabi-Yau metric manifold, including the case when there is a non-trivial H-flux and non-vanishing dilaton. The 4 corresponding BRST charges are well defined on any generalized Kahler manifold. This allows one to consider the half-twisted model defining thus the chiral de Rham complex of a generalized Kahler manifold. The classical limit of this result allows one to recover the celebrated generalized Kahler identities as the degree zero part of an infinite dimensional Lie superalgebra attached to any generalized Kahler manifold. As a byproduct of our study we investigate the properties of generalized Calabi-Yau metric manifolds in the Lie algebroid setting.
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| 35. |
- Hu, Shuangwei
(författare)
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Dynamics of Discrete Curves with Applications to Protein Structure
- 2013
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- In order to perform a specific function, a protein needs to fold into the proper structure. Prediction the protein structure from its amino acid sequence has still been unsolved problem. The main focus of this thesis is to develop new approach on the protein structure modeling by means of differential geometry and integrable theory. The start point is to simplify a protein backbone as a piecewise linear polygonal chain, with vertices recognized as the central alpha carbons of the amino acids. Frenet frame and equations from differential geometry are used to describe the geometric shape of the protein linear chain. Within the framework of integrable theory, we also develop a general geometrical approach, to systematically derive Hamiltonian energy functions for piecewise linear polygonal chains. These theoretical studies is expected to provide a solid basis for the general description of curves in three space dimensions. An efficient algorithm of loop closure has been proposed.
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| 36. |
- Hull, Chris, et al.
(författare)
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Generalized Kahler geometry in (2,1) superspace
- 2012
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Ingår i: Journal of High Energy Physics (JHEP). - 1126-6708 .- 1029-8479. ; :6, s. 13-
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Tidskriftsartikel (refereegranskat)abstract
- Two-dimensional (2, 2) supersymmetric nonlinear sigma models can be described in (2,2), (2, 1) or (1, 1) superspaces. Each description emphasizes different aspects of generalized Kahler geometry. We investigate the reduction from (2,2) to (2, 1) superspace. This has some interesting nontrivial features arising from the elimination of nondynamical fields. We compare quantization in the different superspace formulations.
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| 37. |
- Hull, C. M., et al.
(författare)
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Euclidean supersymmetry, twisting and topological sigma models
- 2008
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Ingår i: Journal of High Energy Physics (JHEP). - : Springer Science and Business Media LLC. - 1126-6708 .- 1029-8479. ; :6, s. 031-
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Tidskriftsartikel (refereegranskat)abstract
- We discuss two dimensional N-extended supersymmetry in Euclidean signature and its R-symmetry. For N = 2, the R-symmetry is SO(2) x SO(1, 1), so that only an A-twist is possible. To formulate a B-twist, or to construct Euclidean N = 2 models with H-flux so that the target geometry is generalised Kahler, it is necessary to work with a complexification of the sigma models. These issues are related to the obstructions to the existence of non-trivial twisted chiral superfields in Euclidean superspace.
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| 38. |
- Hull, Chris M., et al.
(författare)
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Generalized Calabi-Yau metric and generalized Monge-Ampere equation
- 2010
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Ingår i: Journal of High Energy Physics (JHEP). - 1126-6708 .- 1029-8479. ; :8, s. 060-
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Tidskriftsartikel (refereegranskat)abstract
- In the neighborhood of a regular point, generalized Kahler geometry admits a description in terms of a single real function, the generalized Kahler potential. We study the local conditions for a generalized Kahler manifold to be a generalized Calabi-Yau manifold and we derive a non-linear PDE that the generalized Kahler potential has to satisfy for this to be true. This non-linear PDE can be understood as a generalization of the complex Monge-Ampere equation and its solutions give supergravity solutions with metric, dilaton and H-field.
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| 39. |
- Hull, Chris M., et al.
(författare)
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Generalized Kahler geometry and gerbes
- 2009
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Ingår i: Journal of High Energy Physics (JHEP). - : Springer Science and Business Media LLC. - 1126-6708 .- 1029-8479. ; :10, s. 062-
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Tidskriftsartikel (refereegranskat)abstract
- We introduce and study the notion of a biholomorphic gerbe with connection. The biholomorphic gerbe provides a natural geometrical framework for generalized Kahler geometry in a manner analogous to the way a holomorphic line bundle is related to Kahler geometry. The relation between the gerbe and the generalized Kahler potential is discussed.
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| 40. |
- Iakovidis, Nikolaos, et al.
(författare)
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7D supersymmetric Yang-Mills on hypertoric 3-Sasakian manifolds
- 2020
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Ingår i: Journal of High Energy Physics (JHEP). - 1126-6708 .- 1029-8479. ; :6
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Tidskriftsartikel (refereegranskat)abstract
- We study 7D maximally supersymmetric Yang-Mills theory on 3-Sasakian manifolds. For manifolds whose hyper-Kähler cones are hypertoric we derive the perturbative part of the partition function. The answer involves a special function that counts integer lattice points in a rational convex polyhedral cone determined by hypertoric data. This also gives a more geometric structure to previous enumeration results of holomorphic functions in the literature. Based on physics intuition, we provide a factorisation result for such functions. The full proof of this factorisation using index calculations will be detailed in a forthcoming paper.
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| 41. |
- Källén, Johan, et al.
(författare)
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Equivariant Rozansky-Witten classes and TFTs
- 2013
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Ingår i: Journal of Geometry and Physics. - : Elsevier BV. - 0393-0440 .- 1879-1662. ; 64:1, s. 222-242
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Tidskriftsartikel (refereegranskat)abstract
- We first construct the Rozansky-Witten model coupled to BF theory and Chern-Simons theory using the Alexandrov-Kontsevich-Schwarz-Zaboronsky (AKSZ) method. Then we apply the machinery developed in some earlier papers about AKSZ theories and characteristic classes to these concrete models: the BF-Rozansky-Witten model and the Chern-Simons-Rozansky-Witten model. In the former case, we obtain characteristic classes on the target hyperKähler manifold equipped with a group action as a generalization of the original Rozansky-Witten classes. We also give the prescription for similar classes associated with a holomorphic symplectic manifold and demonstrate the invariance of such classes explicitly.
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| 42. |
- Källén, Johan, et al.
(författare)
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N 3-behavior from 5D Yang-Mills theory
- 2012
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Ingår i: Journal of High Energy Physics (JHEP). - 1126-6708 .- 1029-8479. ; 2012:10, s. 184-
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Tidskriftsartikel (refereegranskat)abstract
- In this note we derive N 3-behavior at large 't Hooft coupling for the free energy of 5D maximally supersymmetric Yang-Mills theory on S 5. We also consider a Z κ quiver of this model, as well as a model with M hypermultiplets in the fundamental representation. We compare the results to the supergravity description and comment on their relation.
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| 43. |
- Källén, Johan, et al.
(författare)
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The perturbative partition function of supersymmetric 5D Yang-Mills theory with matter on the five-sphere
- 2012
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Ingår i: Journal of High Energy Physics (JHEP). - 1126-6708 .- 1029-8479. ; :8, s. 157-
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Tidskriftsartikel (refereegranskat)abstract
- Based on the construction by Hosomichi, Seong and Terashima we consider N = 1 supersymmetric 5D Yang-Mills theory with matter on a five-sphere with radius r. This theory can be thought of as a deformation of the theory in flat space with deformation parameter r and this deformation preserves 8 supercharges. We calculate the full perturbative partition function as a function of r/g(YM)(2), where g(YM) is the Yang-Mills coupling, and the answer is given in terms of a matrix model. We perform the calculation using localization techniques. We also argue that in the large N-limit of this deformed 5D Yang-Mills theory this matrix model provides the leading contribution to the partition function and the rest is exponentially suppressed.
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| 44. |
- Källén, Johan, et al.
(författare)
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Twisted supersymmetric 5D Yang-Mills theory and contact geometry
- 2012
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Ingår i: Journal of High Energy Physics (JHEP). - 1126-6708 .- 1029-8479. ; :5, s. 125-
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Tidskriftsartikel (refereegranskat)abstract
- We extend the localization calculation of the 3D Chern-Simons partition function over Seifert manifolds to an analogous calculation in five dimensions. We construct a twisted version of N = 1 supersymmetric Yang-Mills theory defined on a circle bundle over a four dimensional symplectic manifold. The notion of contact geometry plays a crucial role in the construction and we suggest a generalization of the instanton equations to five-dimensional contact manifolds. Our main result is a calculation of the full perturbative partition function on S-5 for the twisted supersymmetric Yang-Mills theory with different Chern-Simons couplings. The final answer is given in terms of a matrix model. Our construction admits generalizations to higher dimensional contact manifolds. This work is inspired by the work of Baulieu-Losev-Nekrasov from the mid 90's, and in a way it is covariantization of their ideas for a contact manifold.
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| 45. |
- Källén, Johan, 1983-
(författare)
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Twisting and Gluing : On Topological Field Theories, Sigma Models and Vertex Algebras
- 2012
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- This thesis consists of two parts, which can be read separately. In the first part we study aspects of topological field theories. We show how to topologically twist three-dimensional N=2 supersymmetric Chern-Simons theory using a contact structure on the underlying manifold. This gives us a formulation of Chern-Simons theory together with a set of auxiliary fields and an odd symmetry. For Seifert manifolds, we show how to use this odd symmetry to localize the path integral of Chern-Simons theory. The formulation of three-dimensional Chern-Simons theory using a contact structure admits natural generalizations to higher dimensions. We introduce and study these theories. The focus is on the five-dimensional theory, which can be understood as a topologically twisted version of N=1 supersymmetric Yang-Mills theory. When formulated on contact manifolds that are circle fibrations over a symplectic manifold, it localizes to contact instantons. For the theory on the five-sphere, we show that the perturbative part of the partition function is given by a matrix model.In the second part of the thesis, we study supersymmetric sigma models in the Hamiltonian formalism, both in a classical and in a quantum mechanical setup. We argue that the so called Chiral de Rham complex, which is a sheaf of vertex algebras, is a natural framework to understand quantum aspects of supersymmetric sigma models in the Hamiltonian formalism. We show how a class of currents which generate symmetry algebras for the classical sigma model can be defined within the Chiral de Rham complex framework, and for a six-dimensional Calabi-Yau manifold we calculate the equal-time commutators between the currents and show that they generate the Odake algebra.
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| 46. |
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| 47. |
- Lindstrom, Ulf, et al.
(författare)
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D-branes in N = 2 WZW models
- 2003
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Ingår i: Phys. Lett.. ; B560, s. 108-115
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Tidskriftsartikel (refereegranskat)
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| 48. |
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| 49. |
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| 50. |
- Lindström, Ulf, et al.
(författare)
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Generalized complex manifolds and supersymmetry
- 2005
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Ingår i: Communications in Mathematical Physics. - : Springer Science and Business Media LLC. - 0010-3616 .- 1432-0916. ; 257, s. 235-256
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Tidskriftsartikel (refereegranskat)abstract
- We find a worldsheet realization of generalized complex geometry, a notion introduced recently by Hitchin which interpolates between complex and symplectic manifolds. The two-dimensional model we construct is a supersymmetric relative of the Poisson sigma model used in context of deformation quantization.
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