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Breaking an Abelian gauge symmetry near a black hole horizon

Steven S. Gubser

TL;DR

The paper investigates whether a charged scalar can condense near the horizon of an AdS4 black hole, spontaneously breaking the U(1) gauge symmetry and signaling holographic superconductivity. It analyzes the RN-AdS4 background and searches for marginally stable, non-backreacting perturbations of the scalar; when the effective mass $m_eff^2 = m^2 + g^{tt} q^2 Phi^2$ becomes negative outside the horizon for large charge $q$ and suitable $m^2$, a near-horizon condensate can form. The results show marginal modes on parameter-space surfaces, with a tower of such modes in AdS4 that disappear in the flat-space limit, indicating the essential role of AdS boundary conditions. The work provides a simple, renormalizable gravity-based mechanism for horizon superconductivity and motivates future holographic studies of transport, vortices, and dual boundary theories.

Abstract

I argue that coupling the Abelian Higgs model to gravity plus a negative cosmological constant leads to black holes which spontaneously break the gauge invariance via a charged scalar condensate slightly outside their horizon. This suggests that black holes can superconduct.

Breaking an Abelian gauge symmetry near a black hole horizon

TL;DR

The paper investigates whether a charged scalar can condense near the horizon of an AdS4 black hole, spontaneously breaking the U(1) gauge symmetry and signaling holographic superconductivity. It analyzes the RN-AdS4 background and searches for marginally stable, non-backreacting perturbations of the scalar; when the effective mass becomes negative outside the horizon for large charge and suitable , a near-horizon condensate can form. The results show marginal modes on parameter-space surfaces, with a tower of such modes in AdS4 that disappear in the flat-space limit, indicating the essential role of AdS boundary conditions. The work provides a simple, renormalizable gravity-based mechanism for horizon superconductivity and motivates future holographic studies of transport, vortices, and dual boundary theories.

Abstract

I argue that coupling the Abelian Higgs model to gravity plus a negative cosmological constant leads to black holes which spontaneously break the gauge invariance via a charged scalar condensate slightly outside their horizon. This suggests that black holes can superconduct.

Paper Structure

This paper contains 4 sections, 20 equations, 2 figures.

Table of Contents

  1. Introduction
  2. The Reissner-Nordstrom black hole in $AdS_4$
  3. Marginally stable modes
  4. Conclusions

Figures (2)

  • Figure 1: Examples of marginally stable modes in an asymptotically $AdS_4$ geometry.
  • Figure 2: The Penrose diagram of a static black hole horizon. Each point in the regions on the right and the top represents a two-dimensional slice at constant $t$ and $r$ of the metric (\ref{['RNAdS']}). The other two regions arise from continuing the metric to a spacetime whose only failures to be geodesically complete arise from curvature singularities. The region on the right connects to asymptotic infinity and corresponds to $r>r_H$. Contours of constant $t$ are shown in this region.