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Holographic striped phases

Aristomenis Donos, Jerome P. Gauntlett

TL;DR

Donos and Gauntlett identify a new holographic mechanism for striped phases in $d=3$ CFTs by showing that neutral pseudo-scalar couplings to gauge fields on $D=4$ AdS-RN black branes generate instabilities at finite momentum. Their analysis uses both the IR $AdS_{2}\times\mathbb{R}^{2}$ BF bound and full AdS-RN perturbations, revealing that the onset of stripes involves a current density wave at $k_c$ and a charge density wave at $2k_c$, with corresponding spatially modulated vevs. They demonstrate this mechanism in a broad class of models, including the top-down skew-whiffed $AdS_4\times SE_7$ reductions, and extend the discussion to theories with two vector fields where additional couplings can drive similar instabilities. The results indicate a competition between striped phases and superfluid instabilities, motivating further work on thermodynamics and fully backreacted solutions to map the phase structure and potential connections to condensed matter systems such as heavy fermion materials and cuprates.

Abstract

We discuss new types of instabilities of D=4 electrically charged AdS-Reissner-Nordström black branes that involve neutral pseudo-scalars. The instabilities spontaneously break translational invariance and are associated with the dual three-dimensional CFTs, at finite temperature and fixed chemical potential with respect to a global abelian symmetry, acquiring striped phases. We show that such instabilities are present for the infinite class of skew-whiffed $AdS_4\times SE_7$ solutions of D=11 supergravity, albeit at a lower temperature than the known superfluid instabilities.

Holographic striped phases

TL;DR

Donos and Gauntlett identify a new holographic mechanism for striped phases in CFTs by showing that neutral pseudo-scalar couplings to gauge fields on AdS-RN black branes generate instabilities at finite momentum. Their analysis uses both the IR BF bound and full AdS-RN perturbations, revealing that the onset of stripes involves a current density wave at and a charge density wave at , with corresponding spatially modulated vevs. They demonstrate this mechanism in a broad class of models, including the top-down skew-whiffed reductions, and extend the discussion to theories with two vector fields where additional couplings can drive similar instabilities. The results indicate a competition between striped phases and superfluid instabilities, motivating further work on thermodynamics and fully backreacted solutions to map the phase structure and potential connections to condensed matter systems such as heavy fermion materials and cuprates.

Abstract

We discuss new types of instabilities of D=4 electrically charged AdS-Reissner-Nordström black branes that involve neutral pseudo-scalars. The instabilities spontaneously break translational invariance and are associated with the dual three-dimensional CFTs, at finite temperature and fixed chemical potential with respect to a global abelian symmetry, acquiring striped phases. We show that such instabilities are present for the infinite class of skew-whiffed solutions of D=11 supergravity, albeit at a lower temperature than the known superfluid instabilities.

Paper Structure

This paper contains 8 sections, 36 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Einstein-Maxwell-pseudo-scalar model
  3. Perturbative instabilities of $AdS_{2}\times \mathbb{R}^{2}$
  4. Perturbative instabilities of the AdS-RN black brane
  5. Stripes
  6. A pseudo-scalar coupled to two vector fields
  7. Discussion
  8. A converse result

Figures (2)

  • Figure 1: The shaded region in the $(\tilde{m}_{s}^{2}, c_{1})$ plane has unstable perturbative modes in the $AdS_{2}\times \mathbb{R}^{2}$ background. The green region has unstable modes including $k=0$ while the cyan region only has unstable modes with $k\ne 0$. The blue circle, lying just inside the cyan region, represents the model associated with skew-whiffed $AdS_4\times SE_7$ solutions. The other symbols are explained in the text.
  • Figure 2: Plots of critical temperatures $T$ versus $k$ for the existence of normalisable static perturbations about the electrically charged AdS-RN black brane. All cases have $m^2_s=-4$. With reference to figure \ref{['fig:theoryMap']}, figure (a) corresponds to the square, figure (b) corresponds to the rhombi and figure (c) corresponds to the triangles.