Prepotentials for (2,2) Supergravity

TL;DR

This paper provides a comprehensive solution to the constraints of two-dimensional N=2 supergravity in superspace, explicitly expressing covariant derivatives using superfields, and distinguishes two minimal supergravity versions.

Contribution

It offers explicit formulations of covariant derivatives in N=2 supergravity and clarifies the structure of minimal (2,2) supergravity variants.

Findings

Explicit expressions for covariant derivatives in terms of superfields.

Complete solution to the constraints of 2D N=2 supergravity.

Differentiation between chiral and twisted chiral superfield formulations.

Abstract

We present a complete solution of the constraints for two-dimensional, N=2 supergravity in N=2 superspace. We obtain explicit expressions for the covariant derivatives in terms of the vector superfield $H^m$ and, for the two versions of minimal (2,2) supergravity, a chiral or twisted chiral scalar superfield $\phi$.