Gravity Dual of Spatially Modulated Phase

TL;DR

This paper demonstrates that in a holographic setup, a large Chern-Simons coupling induces an instability in charged black holes, leading to a spatially modulated phase with spontaneous current in the dual quantum field theory.

Contribution

It reveals a new mechanism for spatially modulated phases via Chern-Simons induced instabilities in holographic models.

Findings

Chern-Simons term causes tachyonic instability at finite momentum.

Instability leads to a helical current phase in the dual field theory.

Three-charge black holes are near the stability threshold.

Abstract

We show that the five-dimensional Maxwell theory with the Chern-Simons term is tachyonic in the presence of a constant electric field. When coupled to gravity, a sufficiently large Chern-Simons coupling causes instability of the Reissner-Nordstrom black holes in anti-de Sitter space. The instability happens only at non-vanishing momenta, suggesting a spatially modulated phase in the holographically dual quantum field theory in 3+1 dimensions, with spontaneous current generation in a helical configuration. The three-charge extremal black hole in the type IIB superstring theory on AdS_5 x S^5 barely satisfies the stability condition.