On Large N Solution of Gaiotto-Tomasiello Theory

TL;DR

This work derives the planar solution for the ${ m N}=3$ GT theory by obtaining a two-cut planar resolvent expressed via contour integrals, and demonstrates that the supersymmetric Wilson loop exhibits AdS-like exponential growth when the total CS level $|k_1+k_2|$ is small. In the decoupling limit $|k_2| oty$, the theory reduces to a single gauge group with fundamental matter, the planar resolvent simplifies to a single-cut form, and the Wilson loop loses its exponential behavior, becoming at most power-like. The analysis connects GT theory to ABJ/ABJM structures and provides insight into how Romans mass and massive Type IIA backgrounds influence Wilson-loop dynamics in the planar regime. These results illuminate the role of fundamental matter in AdS/CFT-like expectations for Chern-Simons-matter theories and propose pathways to extend the approach to other quiver theories and their gravity duals.

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.