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
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
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