Low-energy dynamics of condensed matter from the high-energy point of view: Studies in the effective field theory of matter

Abstract

In this work, we develop effective field theory (EFT) methods for the study of a widevariety of condensed matter systems, including superfluids, ordinary fluids, solids, and super-solids. As a first application, we focus on the dynamics of vortex lines in trapped superfluidcondensates, studying their precessional motion and working out the frequency of precessionfrom EFT principles. We consider the effects of trapping in two and three dimensions, aswell as implications of trapping for the dispersion relation of Kelvin waves along superfluidvortex lines. We also apply our formalism to study the effects of gravitational fields on soundwaves in several different media, discovering that localized sound waves propagate with anassociated (negative) net mass, which in turn generates a tiny gravitational field. We con-firm that this effect is a robust result that can be found from purely classical, non-relativisticmethods. We then present three Lorentz invariant, renormalizable, weakly coupled theoriesthat implement the symmetry-breaking pattern of a perturbative homogeneous and isotropicsolid, as potential UV-completions of the low-energy effective theory that we studied. Wedemonstrate that a particular class of homogeneous, isotropic solids at long distances cor-responds to states that are also homogeneous at short distances, unlike typical solids foundin nature. We find that each case leads to the same rather unorthodox effective theory of asolid with luminal transverse excitations. Finally, we discuss applications of the methods wehave developed and the potential for interesting new directions of this research.