# Mass Deformations of the ABJM Theory: The Holographic Free Energy

## TL;DR

This paper constructs new supersymmetric solutions in supergravity that correspond to mass-deformed ABJM theories, and confirms their free energy matches localization results at large N.

## Contribution

It introduces a new class of supergravity solutions representing mass deformations of ABJM theory with arbitrary R-charges, and verifies their free energy matches field theory calculations.

## Key findings

- New supersymmetric Euclidean solutions in supergravity.
- Agreement between holographic free energy and localization results.
- General mass-deformation parameters for ABJM theory.

## Abstract

We find a class of new supersymmetric Euclidean solutions in four-dimensional maximal gauged supergravity. The holographic dual description of these backgrounds is given by a mass-deformation of the ABJM theory with general values for the R-charges. We calculate the $S^3$ free energy for the supergravity backgrounds and find agreement with the supersymmetric localization calculation of the free energy in the large $N$ limit.