Equivariant localization and gluing rules in 4d $\mathcal{N}=2$ higher derivative supergravity

TL;DR

This paper completes the proof of a conjecture about the structure of higher derivative supergravity in four dimensions, using localization and gluing rules, and applies it to holographic M2-brane partition functions.

Contribution

It provides a complete proof of the form of gravitational building blocks in higher derivative supergravity and explores their gluing rules using localization techniques.

Findings

Validated the form of gravitational building blocks in higher derivative supergravity.

Derived gluing rules applicable at any perturbative order in Newton's constant.

Applied results to holographic predictions for supersymmetric M2-brane partition functions.

Abstract

We complete the proof of the conjecture in arXiv:2111.06903 regarding the form of gravitational building blocks in higher derivative supergravity and examine the related gluing rules. The derivation, based on certain assumptions, combines the BVAB equivariant localization formula (on non-compact spaces) and the direct evaluation of the action on the Omega background in AdS$_4$, arXiv:2212.10590. Utilizing the superconformal gravity formalism and avoiding equations of motion ensures our results are valid at any perturbative order in the Newton constant. As an application, we illustrate the holographic predictions for supersymmetric M2-brane partition functions. We conclude with a to-do list of related calculations in effective supergravity and string theory, aiming for full quantum control of BPS backgrounds.