A new look at instantons and large-N limit

Understand

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.