Linearizing Generalized Kahler Geometry

TL;DR

This paper demonstrates that the complex nonlinear structures in generalized Kahler geometry can be locally linearized by representing them as quotients of simpler, non-nonlinear spaces, simplifying their analysis.

Contribution

It provides a method to linearize the nonlinear data of generalized Kahler manifolds through local quotients, enhancing understanding of their geometric structure.

Findings

Nonlinear data arises from quotients of simpler spaces

Local linearization simplifies the analysis of generalized Kahler geometry

Provides a new perspective on the structure of supersymmetric sigma-model target spaces

Abstract

The geometry of the target space of an N=(2,2) supersymmetry sigma-model carries a generalized Kahler structure. There always exists a real function, the generalized Kahler potential K, that encodes all the relevant local differential geometry data: the metric, the B-field, etc. Generically this data is given by nonlinear functions of the second derivatives of K. We show that, at least locally, the nonlinearity on any generalized Kahler manifold can be explained as arising from a quotient of a space without this nonlinearity.