No abstract

We present a sigma model field theoretic realization of Hitchin's generalized complex geometry, which recently has been shown to be relevant in compactifications of superstring theory with fluxes. Hitchin sigma model is closely related to the well known Poisson sigma model, of which it has the same field content. The construction shows a remarkable correspondence between the (twisted) integrability conditions of generalized almost complex structures and the restrictions on target space geometry implied by the Batalin-Vilkovisky classical master equation. Further, the (twisted) classical Batalin-Vilkovisky cohomology is related non trivially to a generalized Dolbeault cohomology. MSC-class: 53D17, 53B50. Keywords: Poisson Sigma Model, Generalized Complex Geometry, Cohomology.A generalized complex structure J is a section of C ∞ (End(T M ⊕ T * M )), which is an isometry of the metric , and satisfies J 2 = −1.(2.5)The group of isometries of , acts on J by conjugation. In particular, the b transform of J is defined byĴ = exp(−b)J exp(b).(2.6)

We use the AdS/CFT correspondence to calculate three point functions of chiral

I show that the generalized Beltrami differentials and projective connections which appear naturally in induced light cone W n gravity are geometrical fields parametrizing in one-to-one fashion generalized projective structures on a fixed base Riemann surface. I also show that W n symmetries are nothing but gauge transformations of the flat SL(n, C) vector bundles canonically associated to the generalized projective structures. This provides an original formulation of classical light cone W n geometry. From the knowledge of the symmetries, the full BRS algebra is derived. Inspired by the results of recent literature, I argue that quantum W n gravity may be formulated as an induced gauge theory of generalized projective connections. This leads to projective field theory. The possible anomalies arising at the quantum level are analyzed by solving Wess-Zumino consistency conditions. The implications for induced covariant W n gravity are briefly discussed. The results presented, valid for arbitrary n, reproduce those obtained for n = 2, 3 by different methods.