N=2 Conformal SYM theories at large N

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.

58 pages, several figures. v2: some comments added in the Conclusion section, a few references added. Version to be published on JHEP

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• Three-point functions in a $\mathcal{N}=2$ superconformal gauge theory and their strong-coupling limit
• Strong coupling expansions in $\mathcal{N}=2$ quiver gauge theories
• Exact strong coupling results in $\mathcal{N}$=2 $Sp(2N)$ superconformal gauge theory from localization
• Wilson loops in circular quiver SCFTs at strong coupling
• The planar limit of $\mathcal{N}=2$ chiral correlators
• OPE coefficients in Argyres-Douglas theories
• Integrated correlators at strong coupling in an orbifold of $\mathcal{N}=4$ SYM
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• Defect correlators in a $\mathcal{N}=2$ SCFT at strong coupling
• Integrated correlators with a Wilson line in a $\mathcal{N}=2$ quiver gauge theory at strong coupling
• On topological recursion for Wilson loops in $\mathcal{N}=4$ SYM at strong coupling
• Wilson loop correlators in $\mathcal{N}=2$ superconformal quivers
• Exploring superconformal Yang-Mills theories through matrix Bessel kernels
• A derivation of the planar limit of $\mathcal{N}=2$ chiral correlators
• Chiral correlators in $\mathcal{N}=2$ superconformal quivers
• Integrated correlators of coincident Wilson lines in $SU(N)$ gauge theories at strong coupling
• BPS Wilson loop in $\mathcal{N}=2$ superconformal $SU(N)$ "orientifold" gauge theory and weak-strong coupling interpolation
• Loop equations for generalised eigenvalue models
• Strong-coupling results for $\mathcal{N}=2$ superconformal quivers and holography
• Strong coupling expansion of free energy and BPS Wilson loop in $\mathcal{N}=2$ superconformal models with fundamental hypermultiplets
• On the planar free energy of matrix models