Five-dimensional Supergravity Dual of a-Maximization

TL;DR

The paper establishes a concrete holographic realization of a-maximization in 4D SCFTs via five-dimensional gauged supergravity, showing that the a-function maps to the inverse cube of the 5D superpotential and that the superconformal R-symmetry emerges from an attractor condition. It extends the dictionary to include a Lagrange-multiplier formulation, identifying the multipliers with bulk gauge couplings and explaining how anomalous currents are realized in the gravity dual. By analyzing the spectra of vector- and hypermultiplets at AdS5 vacua, the work links operator dimensions and R-charges to bulk scalars and clarifies the holographic counterparts of marginal deformations. The results provide a precise geometric framework for a-maximization within AdS5/CFT4 and suggest directions for incorporating anomalies and higher-derivative corrections in the holographic setup.

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.