T-duality, quotients and generalized Kähler geometry

Merrell, Willie; Vaman, Diana

doi:10.1016/j.physletb.2008.06.031

Cited by 11 publications

(17 citation statements)

References 28 publications

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“…In showing that the structure (26) is preserved by the quotient, we have actually not made use of the fact that c is a constant. Thus, one could in principle extended our results to bihermitean geometries satisfying (26), other than hyperkähler (with c an arbitrary function), if there are any such manifolds. This, however, is not the case due to the following result [18].…”

Section: The Semichiral Quotientmentioning

confidence: 92%

The semi-chiral quotient, hyperkähler manifolds and T-duality

Crichigno

2012

J. High Energ. Phys.

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We study the construction of generalized Kähler manifolds, described purely in terms of N = (2, 2) semichiral superfields, by a quotient using the semichiral vector multiplet. Despite the presence of a b-field in these models, we show that the quotient of a hyperkähler manifold is hyperkähler, as in the usual hyperkähler quotient. Thus, quotient manifolds with torsion cannot be constructed by this method. Nonetheless, this method does give a new description of hyperkähler manifolds in terms of two-dimensional N = (2, 2) gauged non-linear sigma models involving semichiral superfields and the semichiral vector multiplet. We give two examples: Eguchi-Hanson and Taub-NUT. By T-duality, this gives new gauged linear sigma models describing the T-dual of Eguchi-Hanson and NS5-branes. We also clarify some aspects of T-duality relating these models to N = (4, 4) models for chiral/twisted-chiral fields and comment briefly on more general quotients that can give rise to torsion and give an example. 1 crichigno@max2.physics.sunysb.edu Recent developments in both physics and mathematics are renewing the interest in general d = 2, N = (2, 2) sigma models. From the physics perspective, these models describe string compactifications with NS-NS fluxes and, from the mathematics perspective, they provide a useful tool in exploring aspects of Generalized Complex Geometry. This is an example of the interesting interplay between geometry and supersymmetry, initiated by Zumino in the classic work [1]. It is well known by now that the conditions under which d = 2, N = (1, 1) sigma models (with no Wess-Zumino term) admit an extended supersymmetry, can be solved by requiring the target space to be Kähler, for the case of N = (2, 2), and hyperkähler for N = (4, 4) [2]. The action for the sigma model is then simply given by the Kähler potential K(Φ a ,Φ a ) of the target space, with the complex coordinates Φ a identified with N = (2, 2) chiral superfields satisfyingD + Φ a =D − Φ a = 0. These ideas lead to a variety of applications of supersymmetric methods to Kähler geometry. An example of this is the hyperkähler quotient [3,4]. This method is based on the gauging of isometries along directions parametrized by chiral superfields and provides a powerful method for constructing potentials describing hyperkähler manifolds.

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Section: The Semichiral Quotientmentioning

confidence: 92%

The semi-chiral quotient, hyperkähler manifolds and T-duality

Crichigno

2012

J. High Energ. Phys.

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“…We note that promoting the FI parameter t to a twisted chiral field χ corresponds to constraining both field strengths in the SVM to vanish, i.e., performing a T-duality [6,7]. Thus, the moduli space (4.13) can also be thought of as performing a T-duality of flat space (described in terms of semichiral fields) and taking the slice χ = t.…”

Section: Constrained Svmmentioning

confidence: 99%

“…Our analysis of the geometric structure is performed at the classical level, but we also discuss quantum aspects such as R-symmetry anomalies. We provide an explicit example of a generalized Kähler structure on the conifold.Previous work on GLSMs for semichiral fields includes [3,4]; more general couplings of gauge fields to semichiral fields were discussed in [5][6][7][8][9]. The gauging of sigma models with a Wess-Zumino term was studied in [10,11].…”

mentioning

confidence: 99%

On gauged linear sigma models with torsion

Crichigno

Roček

2015

J. High Energ. Phys.

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We study a broad class of two dimensional gauged linear sigma models (GLSMs) with off-shell N = (2, 2) supersymmetry that flow to nonlinear sigma models (NLSMs) on noncompact geometries with torsion. These models arise from coupling chiral, twisted chiral, and semichiral multiplets to known as well as to a new N = (2, 2) vector multiplet, the constrained semichiral vector multiplet (CSVM). We discuss three kinds of models, corresponding to torsionful deformations of standard GLSMs realizing Kähler, hyperkähler, and Calabi-Yau manifolds. The (2, 2) supersymmetry guarantees that these spaces are generalized Kähler. Our analysis of the geometric structure is performed at the classical level, but we also discuss quantum aspects such as R-symmetry anomalies. We provide an explicit example of a generalized Kähler structure on the conifold.

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“…In [35,36,30] and [31], the underlying gauge theory structure has been developed and T-duality transformations were discussed. We first briefly review the case without boundaries closely following the treatment in [30].…”

Section: Dualizing a Chiral/twisted Chiral Pair To A Semi-chiral Multmentioning

confidence: 99%

AnN= 2 worldsheet approach to D-branes in bihermitian geometries: I. Chiral and twisted chiral fields

Sevrin¹,

Staessens²,

Wijns³

2008

J. High Energy Phys.

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We investigate N = (2, 2) supersymmetric nonlinear σ-models in the presence of a boundary. We restrict our attention to the case where the bulk geometry is described by chiral and twisted chiral superfields corresponding to a bihermitian bulk geometry with two commuting complex structures. The D-brane configurations preserving an N = 2 worldsheet supersymmetry are identified. Duality transformations interchanging chiral for twisted chiral fields and vice versa while preserving all supersymmetries are explicitly constructed. We illustrate our results with various explicit examples such as the WZWmodel on the Hopf surface S 3 ×S 1 . The duality transformations provide e.g new examples of coisotropic A-branes on Kähler manifolds (which are not necessarily hyper-Kähler). Finally, by dualizing a chiral and a twisted chiral field to a semi-chiral multiplet, we initiate the study of D-branes in bihermitian geometries where the cokernel of the commutator of the complex structures is non-empty.

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T-duality, quotients and generalized Kähler geometry

Cited by 11 publications

References 28 publications

The semi-chiral quotient, hyperkähler manifolds and T-duality

The semi-chiral quotient, hyperkähler manifolds and T-duality

On gauged linear sigma models with torsion

AnN= 2 worldsheet approach to D-branes in bihermitian geometries: I. Chiral and twisted chiral fields

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