Kahler Normal Coordinate Expansion in Supersymmetric Theories

TL;DR

This paper extends the Riemann normal coordinate expansion to Kahler manifolds, enabling better background field methods in supersymmetric nonlinear sigma models by preserving complex structure.

Contribution

It introduces a Kahler normal coordinate expansion that maintains complex structure, generalizing previous methods for supersymmetric theories.

Findings

Explicit proof of Kahler normal coordinate existence to all orders

Application to supersymmetric nonlinear sigma models

Enhanced background field method techniques

Abstract

The Riemann normal coordinate expansion method is generalized to a Kahler manifold. The Kahler potential and holomorphic coordinate transformations are used to define a normal coordinate preserving the complex structure. The existence of this Kahler normal coordinate is shown explicitly to all orders. The formalism is applied to background field methods in supersymmetric nonlinear sigma models.