N=2 Conformal SYM theories at large N

TL;DR

This paper analyzes N=2 conformal SU(N) SYM theories at large N using matrix models from localization, deriving explicit perturbative expressions and exploring their convergence and potential holographic duals.

Contribution

It develops improved techniques for studying large-N matrix models in N=2 SYM theories and derives high-order perturbative results for observables.

Findings

Explicit perturbative expressions for observables at large N

Finite radius of convergence of the series

Potential for holographic dual descriptions

Abstract

We consider a class of N=2 conformal SU(N) SYM theories in four dimensions with matter in the fundamental, two-index symmetric and anti-symmetric representations, and study the corresponding matrix model provided by localization on a sphere S4, which also encodes information on flat-space observables involving chiral operators and circular BPS Wilson loops. We review and improve known techniques for studying the matrix model in the large-N limit, deriving explicit expressions in perturbation theory for these observables. We exploit both recursive methods in the so-called full Lie algebra approach and the more standard Cartan sub-algebra approach based on the eigenvalue distribution. The sub-class of conformal theories for which the number of fundamental hypermultiplets does not scale with N differs in the planar limit from the N=4 SYM theory only in observables involving chiral operators of odd dimension. In this case we are able to derive compact expressions which allow to push the small 't Hooft coupling expansion to very high orders. We argue that the perturbative series have a finite radius of convergence and extrapolate them numerically to intermediate couplings. This is preliminary to an analytic investigation of the strong coupling behavior, which would be very interesting given that for such theories holographic duals have been proposed.