Hedgehog black holes and the Polyakov loop at strong coupling
- Stanford Institute for Theoretical Physics, Stanford California 94305-4060 (United States)
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.
- OSTI ID:
- 21210208
- Journal Information:
- Physical Review. D, Particles Fields, Vol. 77, Issue 10; Other Information: DOI: 10.1103/PhysRevD.77.105017; (c) 2008 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); ISSN 0556-2821
- Country of Publication:
- United States
- Language:
- English
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