Approximate symmetries abound in nature. If these symmetries are also spontaneously
broken, the would-be Goldstone modes acquire a small mass, or inverse correlation length …

A bstract Within the framework of holography, the Einstein-Maxwell action with Dirichlet
boundary conditions corresponds to a dual conformal field theory in presence of an external …

We propose a general hydrodynamic framework for systems with spontaneously broken
approximate symmetries. The second law of thermodynamics naturally results in relaxation …

Anomalies are renormalization group invariants that constrain the dynamics of quantum field
theories. We show that certain anomalies for discrete global symmetries imply that the …

A bstract We investigate the properties of pole-skipping of the sound channel in which the
translational symmetry is broken explicitly or spontaneously. For this purpose, we analyze, in …

The Colloquium reviews recent progress in the effective description of strongly correlated
phases of matter with spontaneously broken translations, such as charge density waves or …

We combine hydrodynamic and field theoretic methods to develop a general theory of
phonons as Goldstone bosons in crystals, glasses, and liquids based on nonaffine …

A bstract We construct a theory of hydrodynamic transport for systems with conserved dipole
moment, U (1) charge, energy, and momentum. These models have been considered in the …

We recast superfluid hydrodynamics as the hydrodynamic theory of a system with an
emergent anomalous higher-form symmetry. The higher-form charge counts the winding …

We explore the rich landscape of higher-form and non-invertible symmetries that emerge at
low energies in generic ordered phases. Using that their charge is carried by homotopy …