Exact results in a N=2 superconformal gauge theory at strong coupling

Abstract

We consider the $\mathcal{N}=2$ SYM theory with gauge group SU($N$) and a matter content consisting of one multiplet in the symmetric and one in the anti-symmetric representation. This conformal theory admits a large-$N$ 't Hooft expansion and is dual to a particular orientifold of $Ad{S}_5\times S^5$. We analyze this gauge theory relying on the matrix model provided by localization a la Pestun. Even though this matrix model has very non-trivial interactions, by exploiting the full Lie algebra approach to the matrix integration, we show that a large class of observables can be expressed in a closed form in terms of an infinite matrix depending on the 't Hooft coupling $\lambda$. These exact expressions can be used to generate the perturbative expansions at high orders in a very efficient way, and also to study analytically the leading behavior at strong coupling. We successfully compare these predictions to a direct Monte Carlo numerical evaluation of the matrix integral and to the Padé resummations derived from very long perturbative series, that turn out to be extremely stable beyond the convergence disk $|\lambda |<{\pi }^2$ of the latter.

v2:37 pages, 7 figures, a comment and a few references added

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• Strong coupling expansions in $\mathcal{N}=2$ quiver gauge theories
• Non-planar corrections in orbifold/orientifold $\mathcal{N}=2$ superconformal theories from localization
• The planar limit of $\mathcal{N}=2$ chiral correlators
• Linear Quivers at Large-$N$
• Integrated correlators at strong coupling in an orbifold of $\mathcal{N}=4$ SYM
• OPE coefficients in Argyres-Douglas theories
• Wilson loop correlators at strong coupling in $\mathcal{N}=2$ quiver gauge theories
• 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
• Exploring superconformal Yang-Mills theories through matrix Bessel kernels
• A derivation of the planar limit of $\mathcal{N}=2$ chiral correlators
• Integrated correlators of coincident Wilson lines in $SU(N)$ gauge theories at strong coupling
• Strong-coupling results for $\mathcal{N}=2$ superconformal quivers and holography
• Exploring the twisted sector of ${\mathbb{Z}}_L$ orbifolds: Matching ${\alpha }^{\prime }$-corrections to localisation
• Loop equations for generalised eigenvalue models
• Matrix models for extremal and integrated correlators of higher rank
• On the planar free energy of matrix models
• Exact expressions for $n$-point maximal $U(1{)}_Y$-violating integrated correlators in $SU(N)$ $\mathcal{N}=4$ SYM