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Symmetry breaking and Goldstone bosons in holographic strongly coupled field theories: Relativistic and non-relativistic examples

par Marzolla, Andrea
Président du jury Tytgat, Michel
Promoteur Argurio, Riccardo
Publication Non publié, 2017-09-29

Thèse de doctorat

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Résumé :

In this thesis various holographic models are treated, which describe theories of fields where an internal symmetry is broken, either in relativistic contexts, or in case of violation of the Lorentz invariance.The first chapter opens with the revision of the notion of symmetry breaking in pure relativistic field theory. The case of spontaneous breaking and the Goldstone theorem are discussed, as well as the case of explicit breaking, where precise Ward identities between conserved current correlators and scalar operators loaded under such current are derived in a completely general way.We then consider two examples of non-relativistic field theories, which will be reproduced by holographic models: a model in which the invariance of boosts is broken by the presence of a chemical potential, and a model of Lifshitz's invariant theory. We show the non-relativistic realization of Ward's identities for the symmetry breaking.In the second chapter we briefly introduce the correspondence gravitation / gauge theory and we revise the central tool of this thesis, the holographic renormalization.In the third chapter, we show how to generate field theories with symmetry breaking by coupling a scalar field to a gauge field, and holographically deriving the Ward identities predicted by the field theory arguments, first in the Relativistic case. We also obtain an analytic expression for the scalar two-point function, where we know how to find the massless boson of Goldstone and the mass of linear mass in the explicit breaking parameter Of the Goldstone pseudo-boson, respectively in the purely spontaneous case and in the case of an explicit small break.We also consider the two-dimensional case on the edge, where we find that Coleman's theorem is eluded in the wide limit of $ N $, and Ward's identities are not affected.For non-relativistic cases, we first consider a non-abelian model in which the Lorentz invariance is broken: this situation makes it possible to observe so-called ~ B bosons which exhibit a quadratic dispersion relation and do not respect Not the law of a single Goldstone mode for each broken generator.Finally, we study in detail the holographic renormalization and the two-point functions for a conserved current and various scalar operators in a space-time of Lifshitz. We also find the Ward identities of symmetry breaking in their non-relativistic realization.