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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Cited by in corpus (7)

• Localization vs holography in $4d$ $\mathcal{N}=2$ quiver theories
• Structure constants in $\mathcal{N}=2$ superconformal quiver theories at strong coupling and holography
• Non-planar corrections in orbifold/orientifold $\mathcal{N}=2$ superconformal theories from localization
• The planar limit of $\mathcal{N}=2$ chiral correlators
• A derivation of the planar limit of $\mathcal{N}=2$ chiral correlators
• Strong-coupling results for $\mathcal{N}=2$ superconformal quivers and holography
• On the planar free energy of matrix models