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Quantum critical superconductors in string theory and M-theory

Steven S. Gubser, Silviu S. Pufu, Fabio D. Rocha

TL;DR

The paper constructs zero-temperature domain-wall solutions in five- and four-dimensional gauged supergravity that interpolate between AdS spacetimes, describing finite-density quantum-critical ground states with emergent IR conformal symmetry. In explicit string-theory and M-theory realizations, the authors compute frequency-dependent conductivities that exhibit power-law infrared scaling set by IR perturbations, with Re$\sigma(\omega)\propto \omega^{2\Delta_{\Phi}-d}$ (e.g., $\omega^{5}$ in $AdS_5$ and $\omega^{4}$ in $AdS_4$). They uplift these solutions to type IIB and eleven-dimensional supergravity and discuss stability. A central outcome is the Criticality Pairing Conjecture (CPC), linking finite-density states to IR fixed points across RG flows and suggesting broad tests in holography and related frameworks.

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.

Quantum critical superconductors in string theory and M-theory

TL;DR

The paper constructs zero-temperature domain-wall solutions in five- and four-dimensional gauged supergravity that interpolate between AdS spacetimes, describing finite-density quantum-critical ground states with emergent IR conformal symmetry. In explicit string-theory and M-theory realizations, the authors compute frequency-dependent conductivities that exhibit power-law infrared scaling set by IR perturbations, with Re (e.g., in and in ). They uplift these solutions to type IIB and eleven-dimensional supergravity and discuss stability. A central outcome is the Criticality Pairing Conjecture (CPC), linking finite-density states to IR fixed points across RG flows and suggesting broad tests in holography and related frameworks.

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.

Paper Structure

This paper contains 4 sections, 19 equations, 3 figures.

Table of Contents

  1. Introduction
  2. A string theory example
  3. An M-theory example
  4. Discussion

Figures (3)

  • Figure 1: The string theory domain wall.
  • Figure 2: The real part of the conductivity for string theory domain wall. The dots are numerical results, the dashed line is a $\omega^5$ power law with the coefficient chosen such that the line goes through the first dot in the plot and the solid line is the $AdS_5$ conductivity $\mathop{\rm Re}\nolimits\sigma= \pi L\omega/4\kappa^2$.
  • Figure 3: The real part of the conductivity for M-theory domain wall. The dots are numerical results, the dashed line is a $\omega^4$ power law with the coefficient chosen such that the line goes through the first dot in the plot and the solid line is the $AdS_4$ conductivity $\sigma= 1/2\kappa^2$.