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

TL;DR

This paper models the Polyakov loop in anti-symmetric representations within N=4 SYM theory using a quantum impurity model, matching supergravity dual results and revealing geometric-spectral relationships.

Contribution

It introduces a quantum impurity model approach to compute the Polyakov loop in anti-symmetric representations, connecting geometric parameters to spectral properties and extending to different spatial geometries.

Findings

Agreement with supergravity dual calculations.

Relation between D5-brane azimuth angle and spectral asymmetry.

Applicability to various spatial geometries.

Abstract

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.