Equivariant localization for higher derivative supergravity

TL;DR

This paper develops a method using equivariant localization in conformal supergravity to compute supersymmetric observables in higher derivative supergravity theories, applicable to holography and perturbative expansions.

Contribution

It introduces equivariantly closed forms in D=4, N=2 conformal supergravity, enabling calculations without solving equations of motion, advancing the study of higher derivative supergravity.

Findings

Derived closed-form expressions for supersymmetric observables.

Applied the method to holographic on-shell actions valid to all orders in 1/N.

Provided a new computational framework for higher derivative supergravity.

Abstract

Conformal supergravity provides an effective off-shell formalism to study higher derivative actions. We show that the $D=4$, $\mathcal{N}=2$ theory admits equivariantly closed forms. These may be used to compute closed-form expressions for supersymmetric observables in a general class of supergravity theories with higher derivative couplings, without any need to solve equations of motion. We discuss applications to holography, presenting results for on-shell actions that are conjecturally valid to all orders in the perturbative $1/N$ expansion.