Hedgehog black holes and the Polyakov loop at strong coupling

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.

25 pages, 11 figures; v2: minor clarifications, published version

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Cited by in corpus (11)

• Holographic Duals of Long Open Strings
• Schwarzschild radius from Monte Carlo calculation of the Wilson loop in supersymmetric matrix quantum mechanics
• Renormalized Polyakov Loop in the Deconfined Phase of SU(N) Gauge Theory and Gauge/String Duality
• Phase transition of AdS Schwarzschild black hole and gauge theory dual in presence of external string cloud
• Dissolved deconfinement: Phase Structure of large N gauge theories with fundamental matter
• AdS black holes with higher derivative corrections in presence of string cloud
• Supersymmetric Lifshitz-like backgrounds from N=4 SYM with heavy quark density
• Entropic destruction of heavy quarkonium in heavy quark cloud
• String Gas Shells, their Dual Radiation and Hedgehog Signature Control
• Phase Transitions of a (Super) Quantum Mechanical Matrix Model with a Chemical Potential
• Emergent Lifshitz scaling from N=4 SYM with supersymmetric heavy-quark density