A Note on Holographic Non-Relativistic Goldstone Bosons

Understand

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.