Polyakov loop of antisymmetric representations as a quantum impurity model

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.