The planar limit of $\mathcal{N}=2$ chiral correlators

Abstract

We derive the planar limit of 2- and 3-point functions of single-trace chiral primary operators of $\mathcal{N}=2$ SQCD on $S^4$, to all orders in the 't Hooft coupling. In order to do so, we first obtain a combinatorial expression for the planar free energy of a hermitian matrix model with an infinite number of arbitrary single and double trace terms in the potential; this solution might have applications in many other contexts. We then use these results to evaluate the analogous planar correlation functions on ${\mathbb{R}}^4$. Specifically, we compute all the terms with a single value of the $\zeta$ function for a few planar 2- and 3-point functions, and conjecture general formulas for these terms for all 2- and 3-point functions on ${\mathbb{R}}^4$.

arXiv comment25 pages. v2 : added reference

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• Strong coupling expansions in $\mathcal{N}=2$ quiver gauge theories
• Nonrelativistic CFTs at Large Charge: Casimir Energy and Logarithmic Enhancements
• The planar limit of integrated 4-point functions
• Linear Quivers at Large-$N$
• Integrated correlators at strong coupling in an orbifold of $\mathcal{N}=4$ SYM
• Wilson loop correlators at strong coupling in $\mathcal{N}=2$ quiver gauge theories
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• A derivation of the planar limit of $\mathcal{N}=2$ chiral correlators
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• On the planar free energy of matrix models