Theory of K\"ahler 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 {\it target space field theories} with a similar connection on it. Each theory is a gauge theory (with the gauge group being ${\cal SD}iff $ in the case of $3$-fold). It describes deformations of K\"ahler 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.