A topological sigma model of biKähler geometry

BiKaehler geometry is characterized by a Riemannian metric g_{ab} and twocovariantly 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 ofthe biHermitian geometry of Gates, Hull and Roceck, the most general sigmamodel target space geometry allowing for (2,2) world sheet supersymmetry. Wepresent a sigma model for biKaehler geometry that is topological in thefollowing 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 toa topological term; iv) the resulting field theory depends only on a subset ofthe target space geometrical data. The biKaehler sigma model is obtainable bygauge fixing the Hitchin model with generalized Kaehler target space. Itfurther contains the customary A topological sigma model as a particular case.However, it is not seemingly related to the (2,2) supersymmetric biKaehlersigma model by twisting in general.Comment: 46 pages; Late