Stability of holographic superconductors

Sugumi Kanno; Jiro Soda

doi:10.1103/PhysRevD.82.086003

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Stability of holographic superconductors

Sugumi Kanno, Jiro Soda

DOI 10.1103/PhysRevD.82.086003 · Physical Review D

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Abstract

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.