The coset construction for non-equilibrium systems

TL;DR

This paper introduces a systematic coset construction method for non-equilibrium effective field theories that describe the long-distance, late-time dynamics of relativistic, finite-temperature condensed matter systems, incorporating quantum, thermal fluctuations, and dissipation.

Contribution

It develops a novel coset construction framework for non-equilibrium EFTs on the Schwinger-Keldysh contour, enabling the derivation of new effective theories for various phases of matter.

Findings

Reproduces known EFTs for fluids and superfluids at finite temperature.

Constructs new EFTs for solids, supersolids, and liquid crystal phases.

Provides a versatile tool for studying out-of-equilibrium many-body systems.

Abstract

We propose a systematic coset construction of non-equilibrium effective field theories (EFTs) governing the long-distance and late-time dynamics of relativistic, finite-temperature condensed matter systems. Our non-equilibrium coset construction makes significant advances beyond more standard coset constructions in that it takes advantage of recently-developed techniques, which allow the formulation of non-equilibrium effective actions that account for quantum and thermal fluctuations as well as dissipation. Because these systems exist at finite temperature, the EFTs live on the closed-time-path of the Schwinger-Keldysh contour. Since the coset construction and the non-equilibrium effective actions may be unfamiliar to many readers, we include brief introductions to these topics in an effort to make this paper self-contained. To demonstrate the legitimacy of this coset construction, we successfully reproduce the known EFTs for fluids and superfluids at finite temperature. Then, to demonstrate its utility, we construct novel EFTs for solids, supersolids, and four phases of liquid crystals, all at finite temperature. We thereby combine the non-equilibrium effective action and the coset construction to create a powerful tool that can be used to study many-body systems out of thermal equilibrium.