Theory of K\"ahler Gravity

TL;DR

This paper introduces a background-independent target space field theory related to K"ahler structures, connecting $N=2$ topological conformal field theories with deformations of complex structures, potentially serving as a framework for supersymmetric quantum mechanics.

Contribution

It formulates a novel gauge theory on the space of K"ahler structures with a connection, extending Kodaira Spencer theory to a background-independent setting.

Findings

Defines a family of target space field theories with a connection.

Describes deformations of K"ahler structures akin to Kodaira Spencer theory.

Proposes a link to supersymmetric quantum mechanics.

Abstract

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.