Gravity Dual to a Quantum Critical Point with Spontaneous Symmetry Breaking

Abstract

We consider zero-temperature solutions to the Abelian Higgs model coupled to gravity with a negative cosmological constant. With appropriate choices of parameters, the geometry contains two copies of anti-de Sitter space, one describing conformal invariance in the ultraviolet, and one in the infrared. The effective speed of signal propagation is smaller in the infrared. Green's functions and associated transport coefficients can have unusual power-law scaling in the infrared. We provide an example in which the real part of the conductivity scales approximately as omega;{3.5} for small omega.