A unified field theory of topological defects and non-linear local excitations

Abstract Topological defects and smooth excitations determine the properties of systems showing collective order. We introduce a generic non-singular field theory that comprehensively describes in with O ( n ) broken rotational symmetry. Within this formalism, we explore fast events, such as defect nucleation/annihilation dynamical phase transitions where interplay between topological non-linear is particularly important. To highlight its versatility, apply formalism context Bose-Einstein condensates, active nematics, crystal lattices.