The Polyakov Loop of Anti-symmetric Representations as a Quantum Impurity Model

Understand

The Polyakov loop of an operator in the anti-symmetric representation in N=4 SYM theory on spacial R^3 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 AdS_5 x S^5 black brane background.
• It is shown that the azimuth angle, at which the dual D5-brane wraps the S^5, 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 S^3 or H^3.