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arXiv · 0712.4155

Hedgehog black holes and the Polyakov loop at strong coupling

Matthew Headrick
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Abstract

In N=4 super-Yang-Mills theory at large N, large λ, and finite temperature, the value of the Wilson-Maldacena loop wrapping the Euclidean time circle (the Polyakov-Maldacena loop, or PML) is computed by the area of a certain minimal surface in the dual supergravity background. This prescription can be used to calculate the free energy as a function of the PML (averaged over the spatial coordinates), by introducing into the bulk action a Lagrange multiplier term that fixes the (average) area of the appropriate minimal surface. This term, which can also be viewed as a chemical potential for the PML, contributes to the bulk stress tensor like a string stretching from the horizon to the boundary (smeared over the angular directions). We find the corresponding "hedgehog" black hole solutions numerically, within an SO(6)-preserving ansatz, and derive part of the free energy diagram for the PML. As a warm-up problem, we also find exact solutions for hedgehog black holes in pure gravity, and derive the free energy and phase diagrams for that system.

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Matthew Headrick. 2008-05-20. Hedgehog black holes and the Polyakov loop at strong coupling. https://doi.org/10.1103/physrevd.77.105017

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