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.

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

References in corpus (11)

• Operator Mixing in Large $N$ Superconformal Field Theories on ${\mathbb{S}}^4$ and Correlators with Wilson loops
• N=2 Conformal SYM theories at large N
• Large-N correlation functions in $\mathcal{N}=2$ superconformal QCD
• Wilson Loops in N=2 Superconformal Yang-Mills Theory
• Exact results in a N=2 superconformal gauge theory at strong coupling
• $1/N$ expansion of circular Wilson loop in $\mathcal{N}=2$ superconformal $SU(N)\times SU(N)$ quiver
• On the structure of non-planar strong coupling corrections to correlators of BPS Wilson loops and chiral primary operators
• Two-point correlators in non-conformal $\mathcal{N}=2$ gauge theories
• Structure constants in $\mathcal{N}=2$ superconformal quiver theories at strong coupling and holography
• The planar limit of $\mathcal{N}=2$ chiral correlators
• On the planar free energy of matrix models

Cited by in corpus (8)

• Localization vs holography in $4d$ $\mathcal{N}=2$ quiver theories
• Strong coupling expansions in $\mathcal{N}=2$ quiver gauge theories
• Exact strong coupling results in $\mathcal{N}$=2 $Sp(2N)$ superconformal gauge theory from localization
• 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