Polyakov loop of antisymmetric representations as a quantum impurity model

Abstract

The Polyakov loop of an operator in the antisymmetric representation in N=4 supersymmetric Yang-Mills theory on spacial R3 is calculated, to leading order in 1/N and at large ’t Hooft coupling, by solving the saddle point equations of the corresponding quantum impurity model. Agreement is found with previous results from the supergravity dual, which is given by a D5-brane in an asymptotically AdS5×S5 black brane background. It is shown that the azimuth angle, at which the dual D5-brane wraps the S5, is related to the spectral asymmetry angle in the spectral density associated with the Green’s function of the impurity fermions. Much of the calculation also applies to the Polyakov loop on spacial S3 or H3.