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arXiv:2606.02391

Boulder Lectures on Thermal Dynamics and Hydrodynamic EFTs

Luca V. Delacrétaz

Published Jun 1, 2026• 0 citations
arXivHTMLPDF

Abstract

Fluctuating hydrodynamics emerges in essentially any local many-body system at nonzero temperature. Effective field theory (EFT) approaches enable the quantitative study of this emergence, providing a controlled framework to capture late-time observables. These lectures introduce the organizing principles behind equilibrium and out-of-equilibrium dynamics in these thermalizing systems. A central focus is the modern construction of these EFTs, which frames fluctuating hydrodynamics through the lens of "strong-to-weak" spontaneous symmetry breaking. Drawing examples from both high-energy and condensed matter physics, we show how this paradigm adapts to systems ranging from spin chains to relativistic quantum field theories, including models with generalized symmetries or symmetries with 't Hooft anomalies. Finally, we discuss UV/IR constraints on transport parameters -- viewed as the Wilson coefficients of hydrodynamic EFTs -- both in continuum and on the lattice.

DOI
10.48550/arxiv.2606.02391

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Fluctuating hydrodynamics emerges in essentially any local many-body system at nonzero temperature. Effective field theory (EFT) approaches enable the quantitative study of this emergence, providing a controlled framework to capture late-time observables. These lectures introduce the organizing principles behind equilibrium and out-of-equilibrium dynamics in these thermalizing systems. A central focus is the modern construction of these EFTs, which frames fluctuating hydrodynamics through the lens of "strong-to-weak" spontaneous symmetry breaking. Drawing examples from both high-energy and condensed matter physics, we show how this paradigm adapts to systems ranging from spin chains to relativistic quantum field theories, including models with generalized symmetries or symmetries with 't Hooft anomalies. Finally, we discuss UV/IR constraints on transport parameters -- viewed as the Wilson coefficients of hydrodynamic EFTs -- both in continuum and on the lattice.
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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.
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We review recent progress and a number of future directions for applications of effective field theory methods to condensed matter systems broadly defined. Our emphasis is on areas that have allowed a fertile exchange of ideas between high energy physics and many-body theory. We discuss developments in the effective field theory of spontaneous symmetry breaking, of hydrodynamics and non-equilibrium dynamics more generally, fracton phases of matter, and dualities between 2+1 dimensional field theories. We furthermore discuss the application of effective field theory to non-Fermi liquids, the dynamics of entanglement entropy and to condensed matter aspects of cosmology.
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