Superspace Measures, Invariant Actions, and Component Projection Formulae for (2,2) Supergravity

TL;DR

This paper develops invariant measures and component projection formulae for (2,2) supergravity in superspace, enabling the translation of superspace actions into component form for both minimal and extended theories.

Contribution

It introduces explicit measures and projection formulae for (2,2) supergravity in superspace, including chiral measures and component actions for minimal and extended models.

Findings

Derived invariant measures for full and chiral superspaces.

Provided explicit component projection formulae.

Applied to both minimal and extended supergravity theories.

Abstract

In the framework of the prepotential description of superspace two-dimensional $(2,2)$ supergravity, we discuss the construction of invariant integrals. In addition to the full superspace measure, we derive the measure for chiral superspace, and obtain the explicit expressions for going from superspace actions to component actions. We consider both the minimal $U_A(1)$ and the extended $U_V(1) \otimes U_A(1)$ theories.