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 ${\mathbb{R}}^4$.

25 pages. v2 : added reference

References in corpus (10)

• Sphere Partition Functions and the Zamolodchikov Metric
• $t{t}^{\ast }$ equations, localization and exact chiral rings in 4d N=2 SCFTs
• Exact correlation functions in SU(2) N=2 superconformal QCD
• On the Large $R$-charge Expansion in $\mathcal{N}=2$ Superconformal Field Theories
• M-theoretic matrix models
• Operator Mixing in Large $N$ Superconformal Field Theories on ${\mathbb{S}}^4$ and Correlators with Wilson loops
• Constraints on Chiral Operators in N=2 SCFTs
• Large-N correlation functions in $\mathcal{N}=2$ superconformal QCD
• Exact results in a N=2 superconformal gauge theory at strong coupling
• Wilson loops in terms of color invariants

Cited by in corpus (11)

• Localization vs holography in $4d$ $\mathcal{N}=2$ quiver theories
• Strong coupling expansions in $\mathcal{N}=2$ quiver gauge theories
• The planar limit of integrated 4-point functions
• Integrated correlators at strong coupling in an orbifold of $\mathcal{N}=4$ SYM
• Linear Quivers at Large-$N$
• 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
• 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