Holographic free energy and integrated correlators of ${\cal N}=1^*$ theory

TL;DR

This paper analytically derives the second integrated correlators of ${ m N}=4$ super Yang-Mills theory related to ${ m N}=1^*$ mass deformation, confirming previous supergravity results.

Contribution

It provides the first analytic derivation of these correlators at supergravity tree level, enhancing understanding of holographic free energy in ${ m N}=1^*$ theories.

Findings

Analytic expressions for integrated correlators derived

Results agree with previous supergravity BPS solution studies

Advances the holographic understanding of ${ m N}=1^*$ theories

Abstract

We consider the 2nd integrated correlators of ${\cal N}=4$, $D=4$ super Yang-Mills theory, especially those which can be associated with ${\cal N}=1^*$ mass-deformed theories. We provide an analytic derivation of the integrals at supergravity tree level, which has not been available so far. Our result agrees with the previous results from the study of BPS solutions in the dual supergravity models.