Manifestations of symmetries and their breaking in hydrodynamics and holography

Symmetries are fundamental to physical theories: they are used to classify, constrain and simplify. In reality, however, symmetries tend to be broken; the study of sym- metry breaking thus constitutes an important endeavour. This thesis presents work pertaining to symmetry and symmetry breaking – in particular to their manifestations in relativistic hydrodynamics and holography. Pseudo-spontaneous breaking of U(1) symmetry and phase relaxation are studied by extending the hydrodynamic analysis of superfluids. For sufficiently small explicit breaking parameters a hydrodynamic regime may be approximated. The hydrody- namic modes display the effects of pseudo-spontaneous symmetry breaking and phase relaxation. It is furthermore shown that, in the probe limit and in the absence of charge relaxation, the DC conductivity becomes finite but nevertheless the AC conductivity does not present a Drude-peak.