Relativistic Fluids, Superfluids, Solids and Supersolids from a Coset Construction

TL;DR

The paper develops a systematic coset construction for the low-energy EFTs of relativistic fluids, superfluids, solids, and supersolids, showing that the resulting actions are the most general functionals allowed by the symmetry breaking patterns. It identifies the fundamental building blocks for each phase, including b and y for fluids, X in finite temperature superfluids, and A_i, B_{ij} for supersolids (with W,Y,Z invariants for solids), and reproduces the known EFT forms S = ∫ d^D x F(b,y) and S = ∫ d^D x F(W,Y,Z). In (1+1)D it re-derives the Wess-Zumino term associated with an anomalous charge, demonstrating that a specific combination S_WZ^(2)+S_WZ^(3) is exactly invariant under Lorentz and chemical shift up to a total derivative. The work also discusses the role of accidental symmetries and outlines future directions for incorporating dissipation and higher-dimensional anomalies within the coset framework, as well as extending to more general symmetry breakings.

Abstract

We provide a systematic coset construction of the effective field theories governing the low-energy dynamics of relativistic fluids and solids, and of their "super" counterparts. These effective theories agree with those previously derived via different techniques. As an application of our methods, we re-derive the Wess-Zumino term relevant for anomalous charge-carrying fluids in (1+1) dimensions.