First-order supersymmetric sigma models and target space geometry

Bredthauer, Andreas; Lindström, Ulf; Persson, Jonas

doi:10.1088/1126-6708/2006/01/144

Cited by 16 publications

(15 citation statements)

References 25 publications

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“…It turns out that the target manifolds in this model define a ͑twisted͒ generalized Kähler structure ͑Gualtieri, 2003͒. Stimulated by this new mathematical language, there has been tremendous progress in defining generalized ͑topological͒ sigma models ͑Kapustin and Li, 2004;Lindstrom et al, 2005Lindstrom et al, , 2007Bredthauer et al, 2006;Pestun, 2007͒. Topological string theory integrates not only over all maps but also over all metrics on ⌺; this is often called a sigma model coupled to two-dimensional gravity. Classically, the sigma model action depends only on the conformal class of the metric, so the integral over metrics reduces to an integral over conformal ͑or complex͒ structures on ⌺.…”

Section: Topological Sigma Models and String Theorymentioning

confidence: 99%

Conifolds and geometric transitions

Gwyn

Knauf

2008

Rev. Mod. Phys.

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Conifold geometries have recieved much attention in string theory and string-inspired cosmology recently, in particular the Klebanov-Strassler background that is known as the "warped throat." This paper provides a pedagogical explanation for the singularity resolution in this geometry and emphasizes its connection to geometric transitions. The first part focuses on the gauge theory dual to the Klebanov-Strassler background, including the T-dual intersecting branes description. Then, a connection to the Gopakumar-Vafa conjecture for open-closed string duality is presented and a series of papers verifying this model on the supergravity level is summarized. An appendix provides extensive background material about conifold geometries. Special attention is given to their complex structures and the supersymmetry conditions on the background flux in constructions with fractional D3-branes on the singular ͑Klebanov-Tseytlin͒ and resolved ͑Pando Zayas-Tseytlin͒ conifolds are reevaluated. In agreement with earlier results, it is shown that only the singular solution allows a supersymmetric flux. However, the importance of using the correct complex structure to reach this conclusion is emphasized.

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Section: Topological Sigma Models and String Theorymentioning

confidence: 99%

Conifolds and geometric transitions

Gwyn

Knauf

2008

Rev. Mod. Phys.

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“…A very interesting analysis presented in [18] showed how the integrability conditions of the generalized complex structure could be understood, at the nonlinear sigma model level, as the conditions for a manifestly (1, 1) supersymmetric model to be (2,2) supersymmetric. In the language of representations it has also become increasingly evident that semi-chiral superfields play a central role [18][19][20][21][22].…”

Section: Introductionmentioning

confidence: 99%

Gauged (2,2) sigma models and generalized Kähler geometry

Merrell

Zayas

Vaman

2007

J. High Energy Phys.

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We gauge the (2, 2) supersymmetric non-linear sigma model whose target space has bihermitian structure (g, B, J ± ) with noncommuting complex structures. The bihermitian geometry is realized by a sigma model which is written in terms of (2, 2) semi-chiral superfields. We discuss the moment map, from the perspective of the gauged sigma model action and from the integrability condition for a Hamiltonian vector field. We show that for a concrete example, the SU (2) × U (1) WZNW model, as well as for the sigma models with almost product structure, the moment map can be used together with the corresponding Killing vector to form an element of T ⊕ T * which lies in the eigenbundle of the generalized almost complex structure. Lastly, we discuss T-duality at the level of a (2, 2) sigma model involving semi-chiral superfields and present an explicit example.

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“…Such a realization would also shed light on the question of when the second supersymmetry closes off-shell, a question left open in [9]. Such generalized sigma model, with fields transforming also in the cotangent space, was constructed in [14] and studied from the GKG point of view in [15], [3], [5]. For certain models with less supersymmetry a direct relation to GCG was found.…”

Section: Introductionmentioning

confidence: 99%

Generalized Kähler Geometry from Supersymmetric Sigma Models

et al. 2006

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We give a physical derivation of generalized Kähler geometry. Starting from a supersymmetric nonlinear sigma model, we rederive and explain the results of Gualtieri [10] regarding the equivalence between generalized Kähler geometry and the bi-hermitean geometry of Gates-Hull-Roček [9]. 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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First-order supersymmetric sigma models and target space geometry

Cited by 16 publications

References 25 publications

Conifolds and geometric transitions

Conifolds and geometric transitions

Gauged (2,2) sigma models and generalized Kähler geometry

Generalized Kähler Geometry from Supersymmetric Sigma Models

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