Superform Approach to Equivariant Localization in Supergravity

TL;DR

This paper reveals a superspace mechanism enabling equivariant localization in supergravity, constructing equivariantly closed polyforms for various multiplets and action principles in 4d N=2 conformal supergravity.

Contribution

It introduces a geometric superspace approach to equivariant localization in supergravity, extending previous results and aiding in the study of BPS observables and holography.

Findings

Constructed equivariantly closed polyforms for vector and linear multiplets.

Extended localization techniques to higher-derivative supergravity theories.

Provided a geometric framework for BPS observables in supergravity.

Abstract

We identify a superspace mechanism behind equivariant localization in supergravity. We show that closed superforms generate, on supersymmetric backgrounds, equivariantly closed polyforms. After presenting the general mechanism, we construct such polyforms for vector and linear multiplets, and for chiral and BF action principles, in off-shell $4d$ $\mathcal{N}=2$ conformal supergravity, reproducing and extending recent results. Our construction provides a geometric first step toward equivariant localization of BPS observables in supergravity, including higher-derivative theories, and holography.