A new look at instantons and large-N limit

TL;DR

This paper investigates instantons in the strongly coupled large-N gauge theories, revealing their relation to the 't Hooft limit and orbifold theories, with implications for gauge/gravity duality and QCD.

Contribution

It demonstrates that instanton sectors in the very strongly coupled large-N limit are analytically connected to those in the 't Hooft limit and establishes equivalence between instanton partition functions of orbifold-related theories.

Findings

Instanton effects remain finite in the strongly coupled large-N limit.

Instanton sectors are related via simple analytic continuation.

Orbifold projection relates instanton partition functions of different theories.

Abstract

We analyze instantons in the very strongly coupled large-$N$ limit ($N\to\infty$ with $g^2$ fixed) of large-$N$ gauge theories, where the effect of the instantons remains finite. By using the exact partition function of four-dimensional ${\cal N}=2^*$ gauge theories as a concrete example, we demonstrate that each instanton sector in the very strongly coupled large-$N$ limit is related to the one in the 't Hooft limit ($N\to\infty$ with $g^2N$ fixed) through a simple analytic continuation. Furthermore we show the equivalence between the instanton partition functions of a pair of large-$N$ gauge theories related by an orbifold projection. This can open up a new way to analyze the partition functions of low/non-supersymmetric theories. We also discuss implication of our result to gauge/gravity dualities for M-theory as well as a possible application to large-$N$ QCD.