The superconformal index and localizing higher derivative supergravity

TL;DR

This paper demonstrates how equivariant localization can precisely compute the on-shell action of supersymmetric five-dimensional AdS black holes with higher derivatives, matching dual field theory superconformal index calculations.

Contribution

It introduces a method to compute on-shell actions of complex supergravity solutions using localization, aligning gravitational results with dual field theory indices.

Findings

Exact match between supergravity on-shell action and field theory superconformal index.

Localization technique effectively handles higher derivative corrections.

Results validate the duality in a Cardy-like limit.

Abstract

We show how equivariant localization can be used to compute the on-shell action for supersymmetric $D=5$ $AdS$ rotating, charged black holes in theories of supergravity with higher derivatives. An exact match with a dual field theory computation of the superconformal index in a Cardy-like limit is achieved.