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

Abstract

Abstract Using supersymmetric localization, we consider four-dimensional N $$ \mathcal{N} $$ = 2 superconformal quiver gauge theories obtained from ℤ n $$ {\mathbb{Z}}_n $$ orbifolds of N $$ \mathcal{N} $$ = 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 |λ I | < π2, where λ 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 N $$ \mathcal{N} $$ = 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 N $$ \mathcal{N} $$ = 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.

Keywords

• Supersymmetric Gauge Theory
• AdS-CFT Correspondence