On Large N Solution of Gaiotto-Tomasiello Theory

TL;DR

This paper derives the large N solution for Gaiotto-Tomasiello theory, revealing how Wilson loop expectations behave with varying Chern-Simons levels and their implications for AdS/CFT correspondence.

Contribution

It provides the first explicit large N planar resolvent for Gaiotto-Tomasiello theory using contour integrals.

Findings

Wilson loop expectation grows exponentially when sum of levels is small

Exponential behavior vanishes when one level goes to infinity

Results align with AdS/CFT expectations for certain parameter regimes

Abstract

The planar solution is discussed for an N=3 Chern-Simons-matter theory constructed recently by Gaiotto and Tomasiello. The planar resolvent is obtained in terms of contour integrals. If the sum of two Chern-Simons levels k_1,k_2 is small, the expectation value of a supersymmetric Wilson loop grows exponentially with the total 't Hooft coupling, as is expected from AdS/CFT correspondence. If one of the Chern-Simons levels, say k_2, is taken to infinity, for which one of the 't Hooft coupling constants becomes zero, then the exponential behavior disappears.