Abstract:We consider the interplay between explicit and spontaneous symmetry breaking in strongly coupled field theories. Some well-known statements, such as the Gell-MannOakes-Renner relation, descend directly from the Ward identities and have thus a general relevance. Such Ward identities are recovered in gauge/gravity dual setups through holographic renormalization. In a simple paradigmatic three dimensional toy-model, we find analytic expressions for the two-point correlators which match all the quantum field theoretical expectations. Moreover, we have access to the full spectrum, which is reminiscent of linear confinement.

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.

We present a thorough analysis of the electromagnetic response of strongly coupled neutral plasmas described by the gauge/gravity correspondence. The coupling of the external electromagnetic field with the tower of quasi-normal modes of the plasmas supports the presence of various electromagnetic modes with different properties. Among them we underline the existence of negative refraction with low dissipation for a transverse mode. Previous hydrodynamical approaches have shown the ubiquitous character of negative refraction in charged plasmas and the absence thereof in neutral plasmas. Our results here extend the analysis for neutral plasmas beyond the hydrodynamical regime. As an application of these new insights we briefly discuss the case of the quark gluon plasma in the temperature dominated regime.