Giant graviton expansion from eigenvalue instantons

TL;DR

This paper demonstrates that the giant graviton expansion for finite-$N$ gauge theories' partition functions can be derived from eigenvalue instantons in matrix integrals, providing a new perspective without Hubbard-Stratonovich transformations.

Contribution

It shows that the giant graviton expansion can be obtained directly from eigenvalue instantons, simplifying the derivation process.

Findings

Giant graviton expansion matches eigenvalue instanton calculations.

Eigenvalue instantons reproduce the $e^{-mN}$ corrections.

New perspective avoids Hubbard-Stratonovich transformation.

Abstract

Recently, S. Murthy has proposed a convergent expansion of free partition functions and superconformal indices of finite-$N$ purely adjoint gauge theories based on a Fredholm determinant expansion. This expansion has been dubbed the giant graviton expansion and takes the form of an infinite series of corrections to the $N=\infty$ result, with the $m^\text{th}$ correction being of order $e^{-mN}$. We show that this expansion can be reproduced using eigenvalue instantons in unitary matrix integrals. This perspective allows us to get the giant graviton expansion proposed by S. Murthy without the intermediate step of the Hubbard Stratonovich transformation.