| 1. |
- Davgadorj, Ariunzul, et al.
(författare)
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New techniques for gauge theories in projective superspace
- 2023
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Ingår i: Physical Review D. - : American Physical Society. - 2470-0010 .- 2470-0029. ; 108:6
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Tidskriftsartikel (refereegranskat)abstract
- We introduce new techniques for calculations in gauge theories with extended supersymmetry. We are working in projective superspace where the SUo2 thorn R-symmetry is realized geometrically by including an auxiliary CP1 component in the superspace. Different gauge representations are associated with different dependence on the CP1 coordinate zeta and using contour integrals on CP1 we define natural projection operators on these different representations which leads to elegant formulas for all relevant objects. The new techniques lead to compact expressions for Lagrangians and field strengths in terms of the gauge prepotential but also to effective ways of reducing superspace expressions to components, i.e. to write them in terms of fields transforming covariantly only under a subgroup of the supersymmetry group. We illustrate our findings in several examples in three and four dimensions.
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| 2. |
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| 3. |
- 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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| 4. |
- 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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| 5. |
- 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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| 6. |
- Kuzenko, Sergei M., et al.
(författare)
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New extended superconformal sigma models and quaternion Kahler manifolds
- 2009
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Ingår i: Journal of High Energy Physics (JHEP). - : Springer Science and Business Media LLC. - 1126-6708 .- 1029-8479. ; :9, s. 119-
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Tidskriftsartikel (refereegranskat)abstract
- Quaternion Kahler manifolds are known to be the target spaces for matter hypermultiplets coupled to N = 2 supergravity. It is also known that there is a one-to-one correspondence between 4n-dimensional quaternion Kahler manifolds and those 4(n + 1)dimensional hyperkahler spaces which are the target spaces for rigid superconformal hypermultiplets (such spaces are called hyperkahler cones). In this paper we present a projective-superspace construction to generate a hyperkahler cone M-H(4(n + 1)) of dimension 4(n + 1) from a 2n-dimensional real analytic Kahler-Hodge manifold M-K(2n). The latter emerges as a maximal Kahler submanifold of the 4n-dimensional quaternion Kahler space M-Q(4n) such that its Swann bundle coincides with M-H(4)(n + 1). Our approach should be useful for the explicit construction of new quaternion Kahler metrics. The results obtained are also of interest, e. g., in the context of supergravity reduction N = 2 -> N = 1, or alternatively from the point of view of embedding N = 1 matter-coupled supergravity into an N = 2 theory.
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| 7. |
- Kuzenko, Sergei M., et al.
(författare)
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New supersymmetric sigma-model duality
- 2010
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Ingår i: Journal of High Energy Physics (JHEP). - 1126-6708 .- 1029-8479. ; :10, s. 072-
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Tidskriftsartikel (refereegranskat)abstract
- We study dualities in off-shell 4D N = 2 supersymmetric sigma-models, using the projective superspace approach. These include (i) duality between the real O(2n) and polar multiplets; and (ii) polar-polar duality. We demonstrate that the dual of any superconformal sigma-model is superconformal. Since N = 2 superconformal sigma-models (for which target spaces are hyperkahler cones) formulated in terms of polar multiplets are naturally associated with Kahler cones (which are target spaces for N = 1 superconformal sigma-models), polar-polar duality generates a transformation between different Kahler cones. In the non-superconformal case, we study implications of polar-polar duality for the sigma-model formulation in terms of N = 1 chiral superfields. In particular, we find the relation between the original hyperkahler potential and its dual. As an application of polar-polar duality, we study self-dual models.
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| 8. |
- Kuzenko, Sergei M., et al.
(författare)
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Off-shell superconformal nonlinear sigma-models in three dimensions
- 2011
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Ingår i: Journal of High Energy Physics (JHEP). - 1126-6708 .- 1029-8479. ; :1, s. 146-
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Tidskriftsartikel (refereegranskat)abstract
- We develop superspace techniques to construct general off-shell N <= 4 superconformal sigma-models in three space-time dimensions. The most general N = 3 and N = 4 superconformal sigma-models are constructed in terms of N = 2 chiral superfields. Several superspace proofs of the folklore statement that N = 3 supersymmetry implies N = 4 are presented both in the on-shell and off-shell settings. We also elaborate on (super) twistor realisations for (super) manifolds on which the three-dimensional N-extended superconformal groups act transitively and which include Minkowski space as a subspace.
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| 9. |
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| 10. |
- Lindström, Ulf, et al.
(författare)
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A potential for Generalized Kähler Geometry
- 2007
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Ingår i: IRMA Lect. Math. Theor. Phys. 16. - Zuerich, Switzerland : European Mathematical Society Publishing House.
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Tidskriftsartikel (refereegranskat)abstract
- We show that, locally, all geometric objects of Generalized Kahler Geometry can be derived from a function K, the 'generalized Kahler potential''. The metric g and two-form B are determined as nonlinear functions of second derivatives of K. These nonlinearities are shown to arise via a quotient construction from an auxiliary local product (ALP) space.
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| 11. |
- Lindström, Ulf, et al.
(författare)
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Generalized Kahler geometry and manifest N=(2,2) supersymmetric nonlinear sigma-models
- 2005
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Ingår i: Journal of High Energy Physics. ; 0507, s. 067-
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Tidskriftsartikel (refereegranskat)abstract
- Generalized complex geometry is a new mathematical framework that is useful for describing the target space of N=(2,2) nonlinear sigma-models. The most direct relation is obtained at the N=(1,1) level when the sigma model is formulated with an additional auxiliary spinorial field. We revive a formulation in terms of N=(2,2) semi-(anti)chiral multiplets where such auxiliary fields are naturally present. The underlying generalized complex structures are shown to commute (unlike the corresponding ordinary complex structures) and describe a Generalized Kahler geometry. The metric, B-field and generalized complex structures are all determined in terms of a potential K.
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| 12. |
- Lindström, Ulf, et al.
(författare)
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Generalized Kähler manifolds and off-shell supersymmetry
- 2007
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Ingår i: Communications in Mathematical Physics. - : Springer Science and Business Media LLC. - 0010-3616 .- 1432-0916. ; 269:3, s. 833-849
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Tidskriftsartikel (refereegranskat)abstract
- We solve the long standing problem of finding an off-shell supersymmetric formulation for a general N = (2, 2) nonlinear two dimensional sigma model. Geometrically the problem is equivalent to proving the existence of special coordinates; these correspond to particular superfields that allow for a superspace description. We construct and explain the geometric significance of the generalized Kähler potential for any generalized Kähler manifold; this potential is the superspace Lagrangian.
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| 13. |
- Lindström, Ulf, et al.
(författare)
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Linearizing Generalized Kahler Geometry
- 2007
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Ingår i: Journal of High Energy Physics (JHEP). - : Springer Science and Business Media LLC. - 1126-6708 .- 1029-8479. ; :4, s. 061-
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Tidskriftsartikel (refereegranskat)abstract
- The geometry of the target space of an N = (2, 2) supersymmetry sigma-model carries a generalized Kähler structure. There always exists a real function, the generalized Kähler potential K, that encodes all the relevant local differential geometry data: the metric, the B-field, etc. Generically this data is given by nonlinear functions of the second derivatives of K. We show that, at least locally, the nonlinearity on any generalized Kähler manifold can be explained as arising from a quotient of a space without this nonlinearity.
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| 14. |
- Lindström, Ulf, et al.
(författare)
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New N = (2, 2) vector multiplets
- 2007
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Ingår i: Journal of High Energy Physics (JHEP). - : Springer Science and Business Media LLC. - 1126-6708 .- 1029-8479. ; :8, s. 008-
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Tidskriftsartikel (refereegranskat)abstract
- We introduce two new N = (2, 2) vector multiplets that couple naturally to generalized Kähler geometries. We describe their kinetic actions as well as their matter couplings both in N = (2, 2) and N = (1, 1) superspace.
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| 15. |
- Lindström, Ulf, et al.
(författare)
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Nonabelian generalized gauge multiplets
- 2009
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Ingår i: Journal of High Energy Physics (JHEP). - 1126-6708 .- 1029-8479. ; :2, s. 020-
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Tidskriftsartikel (refereegranskat)abstract
- We give the nonabelian extension of the newly discovered N = (2, 2) two-dimensional vector multiplets. These can be used to gauge symmetries of sigma models on generalized Kahler geometries. Starting from the transformation rule for the nonabelian case we find covariant derivatives and gauge covariant field-strengths and write their actions in N = (2, 2) and N = ( 1, 1) superspace.
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| 16. |
- Lindström, Ulf, et al.
(författare)
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Ricci-flat supertwistor spaces
- 2006
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Ingår i: Journal of High Energy Physics. ; 0601:163
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Tidskriftsartikel (refereegranskat)abstract
- We show that supertwistor spaces constructed as a Kahler quotient of a hyperkahler cone (HKC) with equal numbers of bosonic and fermionic coordinates are Ricci-flat, and hence, Calabi-Yau. We study deformations of the supertwistor space induced from deformations of the HKC. We also discuss general infinitesimal deformations that preserve Ricci-flatness.
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| 17. |
- Lindström, Ulf, et al.
(författare)
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T-duality and generalized Kahler geometry
- 2008
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Ingår i: Journal of High Energy Physics. - 1126-6708. ; :2, s. 056-
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Tidskriftsartikel (refereegranskat)abstract
- We use the new N = ( 2, 2) vector multiplets to clarify T-dualities for generalized Kahler geometries. Following the usual procedure, we gauge isometries of nonlinear sigma-models and introduce Lagrange multipliers that constrain the field-strengths of the gauge fields to vanish. Integrating out the Lagrange multipliers leads to the original action, whereas integrating out the vector multiplets gives the dual action. The description is given both in N = (2, 2) and N = (1, 1) superspace.
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| 18. |
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