Large $N$ correlation functions in $\mathcal{N}=2$ superconformal quivers

Abstract

Using supersymmetric localization, we consider four-dimensional $\mathcal{N}=2$ superconformal quiver gauge theories obtained from ${\mathbb{Z}}_n$ orbifolds of $\mathcal{N}=4$ Super Yang-Mills theory in the large $N$ limit at weak coupling. In particular, we show that: 1) The partition function for arbitrary couplings can be constructed in terms of universal building blocks. 2) It can be computed in perturbation series, which converges uniformly for $|{\lambda }_I|<{\pi }^2$, where ${\lambda }_I$ are the 't Hooft coupling of the gauge groups. 3) The perturbation series for two-point functions can be explicitly computed to arbitrary orders. There is no universal effective coupling by which one can express them in terms of correlators of the $\mathcal{N}=4$ theory. 4) One can define twisted and untwisted sector operators. At the perturbative orbifold point, when all the couplings are the same, the correlators of untwisted sector operators coincide with those of $\mathcal{N}=4$ Super Yang-Mills theory. In the twisted sector, we find remarkable cancellations of a certain number of planar loops, determined by the conformal dimension of the operator.

References in corpus (6)

• Sphere Partition Functions and the Zamolodchikov Metric
• The gravity duals of N=2 superconformal field theories
• $t{t}^{\ast }$ equations, localization and exact chiral rings in 4d N=2 SCFTs
• Exact correlation functions in SU(2) N=2 superconformal QCD
• Operator Mixing in Large $N$ Superconformal Field Theories on ${\mathbb{S}}^4$ and Correlators with Wilson loops
• Large-N correlation functions in $\mathcal{N}=2$ superconformal QCD

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