Three-point functions in a $\mathcal{N}=2$ superconformal gauge theory and their strong-coupling limit

Abstract

We study the 3-point functions of single-trace scalar operators in a four-dimensional $\mathcal{N}=2$ SYM theory with gauge group $\mathrm{SU}(N)$ and matter in the symmetric plus anti-symmetric representation, which has a vanishing $\beta$-function. By mapping this computation to the matrix model arising from localization on a 4-sphere we are able to resum the perturbative expansion in the large-$N$ 't Hooft limit and derive the behavior of the correlators at strong coupling. Finally, by combining our results on the 3-point functions with those on the 2-point functions that have been recently found, we obtain the normalized 3-point coefficients of this conformal field theory at strong coupling and find that they depend in a simple way on the conformal dimensions of the single-trace operators.

arXiv comment38 pages, 10 figures, several footnotes, a couple of references and one appendix added; to be published in JHEP

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• 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
• Defect correlators in a $\mathcal{N}=2$ SCFT at strong coupling
• Integrated correlators of coincident Wilson lines in $SU(N)$ gauge theories at strong coupling
• Loop equations for generalised eigenvalue models