Holography for $\mathcal{N}=1^*$ on $S^4$ and Supergravity

TL;DR

This paper uses holography and supergravity to analytically compute the free energy of a mass-deformed $ ext{N}=4$ super Yang-Mills theory on $S^4$, providing a prediction for the partition function at strong coupling.

Contribution

It presents the first analytical holographic calculation of the $ ext{N}=1^*$ theory's $S^4$ free energy using supergravity solutions, clarifying the large coupling behavior.

Findings

Free energy is quadratic in the mass parameter.

Results are free of unphysical ambiguities.

Provides an analytical prediction for the partition function.

Abstract

We study the $SO(3)$ sector of the $\mathcal{N}=1^*$ mass deformation of $\mathcal{N}=4$ super Yang-Mills on $S^4$. The gravity dual of this sector is $\mathcal{N}=2$ supergravity coupled to two hypermultiplets. The scalar fields in the hypermultiplets span a quaternionic-Kahler manifold that is described by the coset $G_{2,2}/SU(2)\times SU(2)$. We use the $\mathcal{N}=2$ supergravity dual to study field configurations in the bulk that feature analytical solutions, and compute the corresponding $S^4$ free energy using the procedure of holographic renormalization. We find that the free energy of these configurations is quadratic in the mass and show that it is devoid of unphysical ambiguities, hence providing an analytical prediction for the $\mathcal{N}=1$ four-sphere partition function at large 't Hooft coupling in the planar limit.