Two-point correlators in non-conformal $\mathcal{N}=2$ gauge theories

Abstract

We study the two-point correlation functions of chiral/anti-chiral operators in $N=2$ supersymmetric Yang-Mills theories on $R^4$ with gauge group SU(N) and $N_f$ massless hypermultiplets in the fundamental representation. We compute them in perturbation theory, using dimensional regularization up to two loops, and show that field-theory observables built out of dimensionless ratios of two-point renormalized correlators on $R^4$ are in perfect agreement with the same quantities computed using localization on the four-sphere, even in the non-conformal case $N_f\ne 2N$.

arXiv comment57 pages, many figures. v2: version to appear on JHEP. Title changed, a few comments added in sections 2,3,4 to clarify some points

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• A slow review of the AGT correspondence
• $\mathcal{N}=2$ conformal gauge theories at large R-charge: the $SU(N)$ case
• Three-point functions in a $\mathcal{N}=2$ superconformal gauge theory and their strong-coupling limit
• OPE coefficients in Argyres-Douglas theories
• Emitted Radiation and Geometry
• Circular Wilson loop in N=2* super Yang-Mills theory at two loops and localization
• Partition functions of non-Lagrangian theories from the holomorphic anomaly
• On topological recursion for Wilson loops in $\mathcal{N}=4$ SYM at strong coupling
• Wilson loop correlators in $\mathcal{N}=2$ superconformal quivers
• Interpolating Bremsstrahlung function in ABJM
• Chiral correlators in $\mathcal{N}=2$ superconformal quivers
• Strong-coupling results for $\mathcal{N}=2$ superconformal quivers and holography
• Exact expressions for $n$-point maximal $U(1{)}_Y$-violating integrated correlators in $SU(N)$ $\mathcal{N}=4$ SYM