Transverse Goldstone mode in holographic fluids with broken translations

TL;DR

This paper explores low energy shear modes in holographic fluids with spontaneously broken translations, revealing gapless diffusive and vortex modes, and analyzing their behavior under explicit symmetry breaking and strong momentum relaxation.

Contribution

It demonstrates the existence of two decoupled gapless modes in holographic fluids with broken translations and studies their evolution under explicit breaking and momentum relaxation.

Findings

Identified two gapless shear modes: diffusive and vortex-like.

Showed that explicit symmetry breaking gives these modes a small mass gap.

Discovered a diffusive-to-sound crossover in strong momentum relaxation regime.

Abstract

In this paper we investigate the low energy shear modes in fluid systems with spontaneously broken translations by a specific holographic model. In absence of momentum relaxation, we find that there exist two decoupled gapless modes in the transverse channel, one of which is purely diffusive and the other corresponds to vortex like excitations. The diffusive mode is associated with the conservation of momentum and the vortex mode can be viewed as the Goldstone mode of the spontaneous symmetry breaking. Switching on an external source which breaks the translations explicitly but weakly, the would-be gapless modes both get relaxed and acquire a tiny mass gap. Finally, in the strong momentum relaxation regime, we find a (pseudo-)diffusive-to-sound crossover that is set by a momentum gap.