Drinfeld-Sokolov gravity

A lagrangian euclidean model of Drinfeld--Sokolov (DS) reduction leading to general W--algebras on a Riemann surface of any genus is presented. The background geometry is given by the DS principal bundle K associated to a complex Lie group G and an SL(2,\Bbb C) subgroup S. The basic fields are a hermitian fiber metric H of K and a (0,1) Koszul gauge field A^* of K valued in a certain negative graded subalgebra \goth x of \goth g related to \goth s. The action governing the H and A^* dynamics is the effective action of a DS field theory in the geometric background specified by H and A^*. Quantization of H and A^* implements on one hand the DS reduction and on the other defines a novel model of 2d gravity, DS gravity. The gauge fixing of the DS gauge symmetry yields an integration on a moduli space of DS gauge equivalence classes of A^* configurations, the DS moduli space. The model has a residual gauge symmetry associated to the DS gauge transformations leaving a given field A^* invariant. This is the DS counterpart of conformal symmetry. Conformal invariance and certain non perturbative features of the model are discussed in detail

T-duality and Generalized Kahler Geometry

We use newly discovered 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.Comment: 14 pages; published version: some conventions improved, minor clarification

An Alternative Topological Field Theory of Generalized Complex Geometry

We propose a new topological field theory on generalized complex geometry in two dimension using AKSZ formulation. Zucchini's model is $A$ model in the case that the generalized complex structuredepends on only a symplectic structure. Our new model is $B$ model in the case that the generalized complex structure depends on only a complex structure.Comment: 29 pages, typos and references correcte

Topological twisted sigma model with H-flux revisited

In this paper we revisit the topological twisted sigma model with H-flux. We explicitly expand and then twist the worldsheet Lagrangian for bi-Hermitian geometry. we show that the resulting action consists of a BRST exact term and pullback terms, which only depend on one of the two generalized complex structures and the B-field. We then discuss the topological feature of the model.Comment: 16 pages. Appendix adde

Toda Fields on Riemann Surfaces: remarks on the Miura transformation

We point out that the Miura transformation is related to a holomorphic foliation in a relative flag manifold over a Riemann Surface. Certain differential operators corresponding to a free field description of $W$--algebras are thus interpreted as partial connections associated to the foliation.Comment: AmsLatex 1.1, 10 page

AKSZ construction from reduction data

We discuss a general procedure to encode the reduction of the target space geometry into AKSZ sigma models. This is done by considering the AKSZ construction with target the BFV model for constrained graded symplectic manifolds. We investigate the relation between this sigma model and the one with the reduced structure. We also discuss several examples in dimension two and three when the symmetries come from Lie group actions and systematically recover models already proposed in the literature.Comment: 42 page

Reduction and construction of Poisson quasi-Nijenhuis manifolds with background

We extend the Falceto-Zambon version of Marsden-Ratiu Poisson reduction to Poisson quasi-Nijenhuis structures with background on manifolds. We define gauge transformations of Poisson quasi-Nijenhuis structures with background, study some of their properties and show that they are compatible with reduction procedure. We use gauge transformations to construct Poisson quasi-Nijenhuis structures with background.Comment: to appear in IJGMM