On Large N Solution of N=3 Chern-Simons-adjoint Theories

TL;DR

This paper derives the planar resolvent for N=3 U(N)_k Chern-Simons theory with adjoint matter, revealing eigenvalue confinement and non-exponential Wilson loop behavior, challenging expectations from gravity duals.

Contribution

It provides an explicit solution for the resolvent in N=3 Chern-Simons-adjoint theories and analyzes the analytic continuation of the 't Hooft coupling.

Findings

Eigenvalues are confined in a finite region even at large coupling

Wilson loop vev does not grow exponentially as expected from gravity duals

Analytic continuation of the 't Hooft coupling reveals finite eigenvalue support

Abstract

The planar resolvent for N=3 U(N)_k Chern-Simons theory coupled to an arbitrary number of adjoint matters is determined. Analytic continuation of the 't Hooft coupling t is analyzed. The eigenvalue distribution turns out to be confined in a finite region even for a large t. The vev of a Wilson loop does not exhibit an exponential growth although such a behavior would be expected for theories with classical gravity duals.