Quantum critical superconductors in string theory and M-theory

Steven S Gubser,Silviu S Pufu,Fabio D Rocha

doi:10.1016/j.physletb.2009.12.017

Steven S Gubser, Silviu S Pufu + Show 1 more

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https://doi.org/10.1016/j.physletb.2009.12.017

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Journal: Physics Letters B	Publication Date: Dec 17, 2009
Citations: 95	License type: cc-by

Affiliation: Princeton University

Abstract

We construct zero-temperature solutions of supergravity theories in five and four dimensions which interpolate between two copies of anti-de Sitter space, one of which preserves an Abelian gauge symmetry while the other breaks it. These domain wall solutions can be lifted to solutions of type IIB string theory and eleven-dimensional supergravity. They describe quantum critical behavior and emergent relativistic conformal symmetry in a superfluid or superconducting state of a strongly coupled dual gauge theory. We include computations of frequency-dependent conductivities which exhibit power law scaling in the infrared, with exponents determined by irrelevant perturbations to the symmetry-breaking anti-de Sitter background.

Highlights

In [1, 2], explicit examples of superconducting black holes were exhibited in type IIB supergravity and Mtheory, respectively
In [9] it was suggested that emergent conformal symmetry should emerge in the zero-temperature limit of superconducting black holes, provided the scalar potential has a symmetry-breaking minimum
The domain walls we have constructed can be fairly described as superconductors because they spontaneously break the U (1) gauge symmetry associated with the field strength Fμν in (1) and (14)

Summary

INTRODUCTION

In [1, 2], explicit examples of superconducting black holes were exhibited in type IIB supergravity and Mtheory, respectively. In [9] it was suggested that emergent conformal symmetry should emerge in the zero-temperature limit of superconducting black holes, provided the scalar potential has a symmetry-breaking minimum. It is not hard to produce similar numerical evidence in favor of emergent conformal symmetry when there is a symmetry-breaking minimum in the scalar potential; domain wall solutions were constructed in [9] which are, plausibly, the zero-temperature limits of the thermodynamically favored superconducting black holes. The authors of [2] anticipated the quantum critical nature of the zero-temperature limit of the superconducting black holes they studied

A STRING THEORY EXAMPLE

AN M-THEORY EXAMPLE

DISCUSSION