The gravity dual to a quantum critical point with spontaneous symmetry breaking

TL;DR

This work considers zero-temperature solutions to the Abelian Higgs model coupled to gravity with a negative cosmological constant and provides an example in which the real part of the conductivity scales approximately as omega;{3.5} for small omega.

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.

Figures (2)

• Figure 1: An example of a solution connecting two AdS vacua with different effective velocities of signal transmission.
• Figure 2: The real part of $\tilde{\sigma}$ as function of $\omega L$ for the solution displayed in figure \ref{['DOMAINWALL']}. The dots show the result of numerical computation while the solid line is the small $\omega$ power-law behavior $\mathop{\rm Re}\nolimits\tilde{\sigma} \sim \omega^\delta$ with the overall constant chosen so the line passes through the first point. The dashed line shows the high $\omega$ limit $\tilde{\sigma} =1$. Note that there is an ambiguity in the scale of $\omega$, as the scaling symmetries affect it. In this plot the scale is fixed by using the scaling symmetries to ensure that $h \to 1$ and $A(r) - r/L \to 0$ as $r \to +\infty$.