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

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.

20 pages, 2 figures, v2: references added and small changes in text, v3: extended to Polyakov loops on spacial R^3, S^3 or H^3

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• Large rank Wilson loops in N=2 superconformal QCD at strong coupling
• Entanglement of heavy quark impurities and generalized gravitational entropy
• A defect action for Wilson loops
• Holographic flows and thermodynamics of Polyakov loop impurities
• Gluonic fields of a static particle to all orders in 1/N
• $q\bar{q}$ Potential at Finite T and Weak Coupling in $\mathcal{N}=4$
• A Holographic Two-Impurity Kondo Model