A new look at instantons and large-N limit

A bstract We analyze instantons in the very strongly coupled large- N limit ( N → ∞ 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 = 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 → ∞ with g 2 N 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.