Theory of Kahler gravity

In this paper we discuss the connection on a space of N = 2 TCFT's that appears in the context of background (in)dependence. We formulate a family of target space field theories with a Similar connection on it. Each theory is a gauge theory (with the gauge group being S Diff in the case of three-fold). It describes deformations of Kahler structures much like Kodaira Spencer theory describes deformations of the complex structures. It is manifestly background-independent. It appears to be a target space field theory for supersymmetric quantum mechanics.