Note on holographic nonrelativistic Goldstone bosons

Abstract

We consider a holographic setup where relativistic invariance is broken by a chemical potential, and a non-Abelian internal symmetry is broken spontaneously. We use the tool of holographic renormalization in order to infer what can be learned purely by analytic boundary considerations. We find that the expected Ward identities are correctly reproduced. In particular, we obtain the identity which implies the noncommutation of a pair of broken charges, which leads to the presence of Goldstone bosons with quadratic dispersion relations.

First sound in holographic superuids at zero temperature

“…To this end, we will first use a simple scaling argument, valid on a fixed AdS background, to show how the background boundary action depends on the chemical potential µ. Next we will employ similar techniques to those developed in [16][17][18][19][20] to derive the quadratic action for the phonons on the boundary. We will show in particular that one recovers the correct dispersion relation for the first sound of a conformal superfluid.…”

The holographic non-abelian vortex

“…Holographic Goldstone modes have been studied by several authors, e.g. [49,50,51,52,53]. The situation that we study in this section is different from these cases, because our symmetry breaking modes give rise to a degree of freedom which is localized on a topological defect.…”

Are there Goldstone bosons in d≤z+1 ?

“…It would be nevertheless interesting to analyze in more details how this works for low dimensions. Also, the same should be true more specifically for type B Goldstone modes [28][29][30], which enjoy a kinetic term linear in B t .…”