| 1. |
- Alho, Artur, et al.
(författare)
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Self-gravitating static balls of power-law elastic matter
- 2022
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Ingår i: Advances in Theoretical and Mathematical Physics. - 1095-0753 .- 1095-0761. ; 26:9, s. 2885-2908
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Tidskriftsartikel (refereegranskat)abstract
- We study a class of power-law stored energy functions for spher-ically symmetric elastic bodies that includes well-known material models, such as the Saint Venant-Kirchhoff, Hadamard, Signorini and John models. We identify a finite subclass of these stored en-ergy functions, which we call Lamé type, that depend on no more material parameters than the bulk modulus k > 0 and the Pois-son ratio —1 < v < 1/2. A general theorem proving the existence of static self-gravitating elastic balls for some power-law materials has been given elsewhere. In this paper numerical evidence is pro-vided that some hypotheses in this theorem are necessary, while others are not.
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| 2. |
- Arnlind, Joakim, et al.
(författare)
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Projections, modules and connections for the noncommutative cylinder
- 2020
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Ingår i: Advances in Theoretical and Mathematical Physics. - : INT PRESS BOSTON, INC. - 1095-0761 .- 1095-0753. ; 24:3, s. 527-562
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Tidskriftsartikel (refereegranskat)abstract
- We initiate a study of projections and modules over a noncommutative cylinder, a simple example of a noncompact noncommutative manifold. Since its algebraic structure turns out to have many similarities with the noncommutative torus, one can develop several concepts in a close analogy with the latter. In particular, we exhibit a countable number of nontrivial projections in the algebra of the noncommutative cylinder itself, and show that they provide concrete representatives for each class in the corresponding K-0 group. We also construct a class of bimodules endowed with connections of constant curvature. Furthermore, with the noncommutative cylinder considered from the perspective of pseudo-Riemannian calculi, we derive an explicit expression for the Levi-Civita connection and compute the Gaussian curvature.
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| 3. |
- 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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| 4. |
- 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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| 5. |
- 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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| 6. |
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| 7. |
- de la Ossa, Xenia, et al.
(författare)
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Almost contact structures on manifolds with a G(2) structure
- 2022
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Ingår i: Advances in Theoretical and Mathematical Physics. - : INT PRESS BOSTON, INC. - 1095-0761 .- 1095-0753. ; 26:1, s. 143-216
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Tidskriftsartikel (refereegranskat)abstract
- We review the construction of almost contact metric (three-) struc-tures, abbreviated ACM(3)S, on manifolds with a G2 structure. These are of interest for certain supersymmetric configurations in string and M-theory. We compute the torsion of the SU(3) struc-ture associated to an ACMS and apply these computations to het -erotic G2 systems and supersymmetry enhancement. We initiate the study of the space of ACM3Ss, which is an infinite dimensional space with a local product structure and interesting topological features. Tantalising links between ACM3Ss and associative and coassociative submanifolds are observed.
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| 8. |
- de la Ossa, Xenia, et al.
(författare)
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Exploring SU(3) structure moduli spaces with integrable G(2) structures
- 2015
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Ingår i: Advances in Theoretical and Mathematical Physics. - 1095-0761 .- 1095-0753. ; 19:4, s. 837-903
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Tidskriftsartikel (refereegranskat)abstract
- We study the moduli space of SU(3) structure manifolds X that form the internal compact spaces in four-dimensional N = 1/2 domain wall solutions of heterotic supergravity with flux. Together with the direction perpendicular to the four-dimensional domain wall, X forms a non-compact 7-manifold Y with torsionful G(2) structure. We use this G(2) embedding to explore how X(t) varies along paths C(t) in the SU(3) structure moduli space. Our analysis includes the Bianchi identities which strongly constrain the flow. We show that requiring that the SU(3) structure torsion is preserved along the path leads to constraints on the G(2) torsion and the embedding of X in Y. Furthermore, we study flows along which the torsion classes of X go from zero to non-zero values. In particular, we present evidence that the flow of half-flat SU(3) structures may contain Calabi-Yau loci, in the presence of non-vanishing H-flux.
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| 9. |
- Ekholm, Tobias, 1970-, et al.
(författare)
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Higher genus knot contact homology and recursion for colored HOMFLY-PT polynomials
- 2020
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Ingår i: Advances in Theoretical and Mathematical Physics. - : INT PRESS BOSTON, INC. - 1095-0761 .- 1095-0753. ; 24:8, s. 2067-2145
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Tidskriftsartikel (refereegranskat)abstract
- We sketch a construction of Legendrian Symplectic Field Theory (SFT) for conormal tori of knots and links. Using large N duality and Witten's connection between open Gromov-Witten invariants and Chern-Simons gauge theory, we relate the SFT of a link conormal to the colored HOMFLY-PT polynomials of the link. We present an argument that the HOMFLY-PT wave function is determined from SFT by induction on Euler characteristic, and also show how to, more directly, extract its recursion relation by elimination theory applied to finitely many noncommutative equations. The latter can be viewed as the higher genus counterpart of the relation between the augmentation variety and Gromov-Witten disk potentials established in [1] by Aganagic, Vafa, and the authors, and, from this perspective, our results can be seen as an SFT approach to quantizing the augmentation variety.
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| 10. |
- Ekholm, Tobias, 1970-, et al.
(författare)
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Topological Strings, D-Model, and Knot Contact Homology
- 2014
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Ingår i: Advances in Theoretical and Mathematical Physics. - Boston : International Press of Boston. - 1095-0761 .- 1095-0753. ; 18:4, s. 827-956
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Tidskriftsartikel (övrigt vetenskapligt/konstnärligt)abstract
- We study the connection between topological strings and contact homology recently proposed in the context of knot invariants. In particular, we establish the proposed relation between the Gromov-Witten disk amplitudes of a Lagrangian associated to a knot and augmentations of its contact homology algebra. This also implies the equality between the Q-deformed A-polynomial and the augmentation polynomial of knot contact homology (in the irreducible case). We also generalize this relation to the case of links and to higher rank representations for knots. The generalization involves a study of the quantum moduli space of special Lagrangian branes with higher Betti numbers probing the Calabi-Yau. This leads to an extension of SYZ, and a new notion of mirror symmetry, involving higher dimensional mirrors. The mirror theory is a topological string, related to D-modules, which we call the "D-model." In the present setting, the mirror manifold is the augmentation variety of the link. Connecting further to contact geometry, we study intersection properties of branches of the augmentation variety guided by the relation to D-modules. This study leads us to propose concrete geometric constructions of Lagrangian fillings for links. We also relate the augmentation variety with the large N limit of the colored HOMFLY, which we conjecture to be related to a Q-deformation of the extension of A-polynomials associated with the link complement.
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