A Note on Holographic Non-Relativistic Goldstone Bosons

TL;DR

This paper uses holographic methods to analyze non-relativistic Goldstone bosons arising from spontaneous symmetry breaking with broken relativistic invariance, confirming expected Ward identities and quadratic dispersion relations.

Contribution

It demonstrates how holographic renormalization can analytically derive properties of non-relativistic Goldstone bosons in a symmetry-breaking setup.

Findings

Ward identities are correctly reproduced.

Goldstone bosons exhibit quadratic dispersion relations.

Non-commuting broken charges lead to non-relativistic Goldstone modes.

Abstract

We consider a holographic set-up 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 non-commutation of a pair of broken charges, which leads to the presence of Goldstone bosons with quadratic dispersion relations.