A topological sigma model of biKaehler geometry

Abstract

BiKaehler geometry is characterized by a Riemannian metric g_{ab} and two covariantly constant generally non commuting complex structures K_+^a_b, K_-^a_b, with respect to which g_{ab} is Hermitian. It is a particular case of the biHermitian geometry of Gates, Hull and Roceck, the most general sigma model target space geometry allowing for (2,2) world sheet supersymmetry. We present a sigma model for biKaehler geometry that is topological in the following sense: i) the action is invariant under a fermionic symmetry delta; ii) delta is nilpotent on shell; iii) the action is delta--exact on shell up to a topological term; iv) the resulting field theory depends only on a subset of the target space geometrical data. The biKaehler sigma model is obtainable by gauge fixing the Hitchin model with generalized Kaehler target space. It further contains the customary A topological sigma model as a particular case. However, it is not seemingly related to the (2,2) supersymmetric biKaehler sigma model by twisting in general.

46 pages; Latex

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• Gauging the Poisson sigma model
• Brackets, Sigma Models and Integrability of Generalized Complex Structures
• Geometric Transitions on non-Kaehler Manifolds
• Black hole entropy and topological strings on generalized CY manifolds
• BiHermitian Supersymmetric Quantum Mechanics
• Generalised HyperKaehler Manifolds in String Theory
• The Lie algebroid Poisson sigma model
• Topological twisted sigma model with H-flux revisited
• An Alternative Topological Field Theory of Generalized Complex Geometry
• A heterotic sigma model with novel target geometry