  In N=4 super-Yang-Mills theory at large N, large \lambda, 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.

High Energy Physics - Theory