# Perturbative solutions of ${\cal N}=1^*$ holography on $S^4$

## TL;DR

This paper develops a perturbative method to solve supergravity equations for ${
m N}=1^*$ theories on $S^4$, providing exact and numerical results for the free energy's universal part as a function of mass parameters.

## Contribution

It introduces a perturbative approach to solve supergravity BPS equations in ${
m N}=1^*$ holography, with exact and numerical calculations of free energy coefficients.

## Key findings

- Exact coefficients of leading quartic terms in free energy obtained.
- Numerical coefficients of higher order terms up to 10th order computed.
- Results enhance understanding of holographic free energy dependence on mass parameters.

## Abstract

We apply the recently proposed perturbative technique to solve the supergravity BPS equations of ${\cal N}=1^*$ theories put on $S^4$. In particular, we have calculated the coefficients of the leading quartic terms exactly, in the expression of the universal part for the holographic free energy as a function of the mass parameters. We also report on the coefficients of higher order terms upto 10th order, which are computed numerically.