Stability of Holographic Superconductors

Details Stability of Holographic Superconductors Stability of Holographic Superconductors

2010-07-28

arxiv.org/abs/1007.5002v2

Phys.Rev.D82:086003,2010

Physics

High Energy Physics

High Energy Physics - Theory

11 pages, published version

Scientific paper

10.1103/PhysRevD.82.086003

We study the dynamical stability of holographic superconductors. We first classify perturbations around black hole background solutions into vector and scalar sectors by means of a 2-dimensional rotational symmetry. We prove the stability of the vector sector by explicitly constructing the positive definite Hamiltonian. To reveal a mechanism for the stabilization of a superconducting phase, we construct a quadratic action for the scalar sector. From the action, we see the stability of black holes near a critical point is determined by the equation of motion for a charged scalar field. We show the effective mass of the charged scalar field in hairy black holes is always above the Breitenlohner-Freedman bound near the critical point due to the backreaction of a gauge field. It implies the stability of the superconducting phase. We also argue that the stability continues away from the critical point.

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