The Holography of F-maximization

TL;DR

This paper constructs new supersymmetric backgrounds in four-dimensional gauged supergravity dual to deformed ABJM theories on S^3, matching supergravity calculations with field theory results via localization.

Contribution

It introduces novel supersymmetric backgrounds in ${ m AdS}_4$ supergravity that correspond to general $U(1)_R$ deformations of ABJM theory on $S^3$, confirming the holographic duality.

Findings

Supergravity backgrounds match field theory free energy calculations.

The work extends holographic duals to more general R-symmetry deformations.

Agreement supports the validity of the supergravity approach for deformed theories.

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.