A new look at instantons and large-N limit

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 $\mathcal{N}=2^{\ast }$ 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 $g^{2}N$ 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.

10 pages

References in corpus (1)

• A new large-N limit and the planar equivalence outside the planar limit

Cited by in corpus (11)

• Quantum Black Hole Entropy from 4d Supersymmetric Cardy formula
• Holography for $\mathcal{N}=2^{\ast }$ on $S^4$
• Harnessing S-Duality in $\mathcal{N}=4$ SYM & Supergravity as $SL(2,\mathbb{Z})$-Averaged Strings
• Holography for $\mathcal{N}=1^{\ast }$ on $S^4$
• Borel summability of perturbative series in 4d N=2 and 5d N=1 theories
• Large $N$ correlation functions in $\mathcal{N}=2$ superconformal quivers
• Modular anomaly equations in N=2* theories and their large-N limit
• Large $N$ expansion of an integrated correlator in $\mathcal{N}=4$ SYM
• S-duality invariant perturbation theory improved by holography
• Brick Walls for Black Holes in AdS/CFT
• One-point functions for doubly-holographic BCFTs and backreacting defects