A topological sigma model of biKaehler geometry

TL;DR

This paper introduces a topological sigma model based on biKaehler geometry, which generalizes known models and depends only on specific geometric data, with potential links to Hitchin's model.

Contribution

It presents a novel topological sigma model for biKaehler geometry, extending the framework of generalized Kähler and Hitchin models, and explores its properties and relations to existing theories.

Findings

The model is invariant under a fermionic symmetry delta.

Delta is nilpotent on shell.

The action is delta-exact on shell up to a topological term.

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.