Spatially modulated instabilities of magnetic black branes

TL;DR

The paper addresses spatially modulated instabilities of magnetically charged AdS black branes and their holographic dual phases. It develops a broad class of gravity theories with two vector fields and a scalar, including top-down truncations, and analyzes linear perturbations around $AdS_{D-2}\times\mathbb{R}^2$ backgrounds to identify BF-bound violating modes at finite momentum. In $D=4$, magnetically charged AdS–RN branes exhibit zero modes leading to current-density waves without charge-density waves, and second-order analysis reveals modulation of the stress tensor and currents; a non-linear ansatz is proposed to capture fully backreacted solutions. A top-down instantiation in type IIB via $D=5$ $SO(6)$ gauged supergravity demonstrates a modulated instability in an $AdS_2\times\mathbb{R}^3$ near-horizon geometry, corresponding to a new phase of $\mathcal{N}=4$ SYM with current-density waves, while final comments outline extensions to fully backreacted solutions and other charge configurations. The results provide concrete holographic realizations of translation-symmetry breaking and enrich the landscape of strongly coupled condensed-matter-like phases.

Abstract

We investigate spatially modulated instabilities of magnetically charged $AdS_{2}\times\mathbb{R}^2$, $AdS_{3}\times\mathbb{R}^2$ and $AdS_{2}\times\mathbb{R}^3$ backgrounds in a broad class of theories, including those arising from KK reductions of ten and eleven dimensional supergravity. We show that magnetically charged black brane solutions in D=4,5 spacetime dimensions, whose zero temperature near horizon limit approach these backgrounds, can have instabilities that are dual to phases with current density waves that spontaneously break translation symmetry. Our examples include spatially modulated instabilities for a new class of magnetic black brane solutions of D=5 SO(6) gauged supergravity, that we construct in closed form, which are dual to new phases of N=4 SYM theory.

Figures (1)

• Figure 1: Plots of critical temperatures $T$ versus $k$ for the existence of normalisable zero modes about the $D=4$ magnetically charged AdS-RN black brane solutions in the models of section \ref{['sec2']}. All cases have $m^2_s=-4$ and $m_{v}^{2}=0$. The left frame has $n=-1$ and, from the top going down, $s= 2,1.9,1.8,1.7$. The right frame has $s=\sqrt{2}$ and, from the top going down, $n= -0.25,-0.375,-0.5,-0.675$. Note that ${\cal N}=8$ gauged supergravity has $n=-1$ and $s=\sqrt {2}$.