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Notes on holographic renormalization as a tool for UV analysis and derivationof the two-point Ward identity encoding symmetry breaking. Goldstone theorem isreviewed, discussing in particular the modifications required by its extensionto non-relativistic field theories. The Ward identity encoding both spontaneousand explicit breaking are derived by general principles. Holographicrenormalization is presented in a quite operational fashion. The derivation ofthe Ward identity in holography is illustrated by an example.

The Ward identity of Symmetry Breaking from Holographic Renormalization