Five-dimensional Supergravity Dual of a-Maximization

TL;DR

This paper explores the duality between five-dimensional supergravity and a-maximization in four-dimensional superconformal field theories, revealing how the extremization principles correspond across the duality.

Contribution

It establishes a precise mapping between a-maximization and the attractor equations in five-dimensional gauged supergravity, including the role of Lagrange multipliers.

Findings

a-maximization corresponds to attractor equations in supergravity

The trial a-function relates to the superpotential's inverse cube

Lagrange multipliers map to gauge couplings in supergravity

Abstract

We study the five-dimensional supergravity dual of the a-maximization under AdS5/CFT4 duality. We firstly show that the a-maximization is mapped to the attractor equation in five-dimensional gauged supergravity, and that the trial a-function is the inverse cube of the superpotential of the five-dimensional theory. There is also a version of a-maximization in which one extremizes over Lagrange multipliers enforcing the anomaly-free condition of the R-symmetry. We identify the supergravity dual of this procedure, and show how the Lagrange multipliers appearing in the supergravity description naturally correspond to the gauge coupling of the superconformal field theory.