The holographic supersymmetric Casimir energy

TL;DR

This paper develops a supersymmetry-preserving holographic renormalization scheme for AdS_5 solutions dual to superconformal field theories on curved backgrounds, accurately reproducing the supersymmetric Casimir energy and BPS relations.

Contribution

It introduces new boundary terms in holographic renormalization that restore supersymmetry for asymptotically AdS_5 solutions, aligning holographic results with field theory expectations.

Findings

Restores supersymmetry in holographic renormalization.

Accurately reproduces supersymmetric Casimir energy.

Validates BPS charge relations in holographic duals.

Abstract

We consider a general class of asymptotically locally AdS_5 solutions of minimal gauged supergravity, that are dual to superconformal field theories on curved backgrounds S^1 x M_3 preserving two supercharges. We demonstrate that standard holographic renormalization corresponds to a scheme that breaks supersymmetry. We propose new boundary terms that restore supersymmetry, and show that for smooth solutions with topology S^1 x R^4 the improved on-shell action reproduces both the supersymmetric Casimir energy and the field theory BPS relation between charges.