The Holography of F-maximization

TL;DR

This paper constructs new Euclidean AdS$_4$ backgrounds within an ${\cal N}=2$ truncation of ${\cal N}=8$ gauged supergravity, dual to the most general $U(1)_R$-preserving deformations of ABJM theory on ${S^3}$. It derives the three complex scalar sector, analyzes the analytic continuation to Euclidean signature, and solves the BPS equations to obtain a three-parameter family of backgrounds. Through careful holographic renormalization and a Legendre transform, the authors compute the ${S^3}$ free energy and demonstrate exact agreement with field theory results obtained via localization and matrix models, including the dependence on R-charges dictated by $F$-maximization. The work clarifies the AdS/CFT dictionary for these deformations, identifies the precise operator-scalar correspondences, and discusses extensions to higher-dimensional lifts and geometric interpretations of the deformations. The study thus provides a quantitative holographic handle on ${F}$-maximization for ABJM at ${k=1}$ and sets a framework for exploring SUSY-preserving deformations on curved spaces.

Abstract

We find new supersymmetric backgrounds of ${\cal N} = 8$ gauged supergravity in four Euclidean dimensions that are dual to deformations of ABJM theory on $S^3$. The deformations encode the most general choice of $U(1)_R$ symmetry used to define the theory on $S^3$. We work within an ${\cal N} = 2$ truncation of the ${\cal N} = 8$ supergravity theory obtained via a group theory argument. We find perfect agreement between the $S^3$ free energy computed from our supergravity backgrounds and the previous field theory computations of the same quantity based on supersymmetric localization and matrix model techniques.