# Solving Mass-deformed Holography Perturbatively

## TL;DR

This paper develops a perturbative approach to solve supergravity BPS equations for mass-deformed holographic duals, successfully reproducing known solutions and deriving new analytic results for free energies in various supersymmetric theories.

## Contribution

It introduces a novel perturbative method for solving supergravity equations related to mass-deformed holography, enabling analytic computation of free energies.

## Key findings

- Reproduces known solutions for mass-deformed ABJM model.
- Derives analytic holographic free energy for Brandhuber-Oz theory.
- Achieves good agreement with localization results for N=2* theory.

## Abstract

We study supergravity BPS equations which correspond to mass-deformation of some representative AdS/CFT examples. The field theory of interest are N=4, D=4 super Yang-Mills, the ABJM model in D=3, and the Brandhuber-Oz fixed point in D=5. For these gauge theories the free energy with mass terms for matter multiplets is calculable in large-N limit using supersymmetric localization technique. We suggest a perturbative method to solve the supergravity equations. For the dual of mass-deformed ABJM model we reproduce the known exact solutions. For the mass-deformed Brandhuber-Oz theory our method gives the holographic free energy in analytic form. For N=2* theory our result is in good agreement with the localization result.