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

Merrell, Willie; Zayas, Leopoldo A. Pando; Vaman, Diana

doi:10.1088/1126-6708/2007/12/039

Cited by 16 publications

(23 citation statements)

References 34 publications

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“…This has led the authors of ref. [9] to extend the analysis of [5] to general biHermitian target spaces. In [10], the same analysis has been carried out in the on-shell formalism.…”

Section: Introductionmentioning

confidence: 99%

Gauging the Poisson sigma model

Zucchini

2008

J. High Energy Phys.

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We show how to carry out the gauging of the Poisson sigma model in an AKSZ inspired formulation by coupling it to a generalization of the Weil model worked out in ref. [31]. We call the resulting gauged field theory, Poisson-Weil sigma model. We study the BV cohomology of the model and show its relation to Hamiltonian basic and equivariant Poisson cohomology. As an application, we carry out the gauge fixing of the pure Weil model and of the Poisson-Weil model. In the first case, we obtain the 2-dimensional version of DonaldsonWitten topological gauge theory, describing the moduli space of flat connections on a closed surface. In the second case, we recover the gauged A topological sigma model worked out by Baptista describing the moduli space of solutions of the so-called vortex equations.Keywords: quantum field theory in curved spacetime; geometry, differential geometry and topology.

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“…This has led the authors of ref. [9] to extend the analysis of [5] to general biHermitian target spaces. In [10], the same analysis has been carried out in the on-shell formalism.…”

Section: Introductionmentioning

confidence: 99%

Gauging the Poisson sigma model

Zucchini

2008

J. High Energy Phys.

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“…ent map with the appropriate mathematical definition. This paper is a follow up to [6], and here we give the answer to the open questions of that previous work. The new ingredient is the use of the appropriate (2,2) semichiral vector multiplet [7,8] for the gauging of the (2,2) supersymmetric semichiral sigma model.…”

Section: Introductionmentioning

confidence: 83%

“…As discussed in [10,6], the gauging of the sigma model can be done most straightforwardly at the level of (2,2) superspace. Here the sigma-model is defined entirely by the Kähler potential, which is a functional of the (2,2) superfields.…”

Section: Superspacementioning

confidence: 99%

T-duality, quotients and generalized Kähler geometry

Merrell

Vaman

2008

Physics Letters B

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In this paper we reopen the discussion of gauging the two-dimensional off-shell (2, 2) supersymmetric sigma models written in terms of semichiral superfields. The associated target space geometry of this particular sigma model is generalized Kähler (or bi-hermitean with two noncommuting complex structures). The gauging of the isometries of the sigma model is now done by coupling the semichiral superfields to the new (2,2) semichiral vector multiplet. We show that the two moment maps together with a third function form the complete set of three Killing potentials which are associated with this gauging. We show that the Killing potentials lead to the generalized moment maps defined in the context of twisted generalized Kähler geometry. Next we address the question of the T-duality map, while keeping the (2,2) supersymmetry manifest. Using the new vector superfield in constructing the duality functional, under T-duality we swap a pair of left and right semichiral superfields by a pair of chiral and twisted chiral multiplets. We end with a discussion on quotient construction.

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“…Integrating out the Lagrange multipliers constrains the (worldsheet) gauge fields to be trivial and so gives back the original model, while integrating out the gauge fields yields the T-dual theory, with the dual geometry given by the Buscher rules [22]. Various gaugings in and out of superspace have been described in [25][26][27][28][29][30][31][32][33][34][35][36][37].…”

Section: Introductionmentioning

confidence: 99%

T-duality in (2, 1) superspace

Abou-Zeid

Hull

Lindström

et al. 2019

J. High Energ. Phys.

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We find the T-duality transformation rules for 2-dimensional (2,1) supersymmetric sigma-models in (2,1) superspace. Our results clarify certain aspects of the (2,1) sigma model geometry relevant to the discussion of T-duality. The complexified duality transformations we find are equivalent to the usual Buscher duality transformations (including an important refinement) together with diffeomorphisms. We use the gauging of sigma-models in (2,1) superspace, which we review and develop, finding a manifestly real and geometric expression for the gauged action. We discuss the obstructions to gauging (2,1) sigma-models, and find that the obstructions to (2,1) T-duality are considerably weaker. 1

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

Cited by 16 publications

References 34 publications

Gauging the Poisson sigma model

Gauging the Poisson sigma model

T-duality, quotients and generalized Kähler geometry

T-duality in (2, 1) superspace

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