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  • Open Access

Building Far-from-Equilibrium Effective Field Theories Using Shift Symmetries

Xin An1,*, Robbe Brants1,†, Michal P. Heller1,2,‡, and Yi Yin3,4,§

  • *Contact author: xin.an@ugent.be
  • †Contact author: robbe.brants@ugent.be
  • ‡Contact author: michal.p.heller@ugent.be
  • §Contact author: yiyin@cuhk.edu.cn
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Phys. Rev. Lett. 137, 192301 – Published 3 November, 2026

DOI: https://doi.org/10.1103/7bz2-nmb9

Abstract

Contemporary understanding of thermalization in quantum field theory stems largely from understanding properties of transient excitations of equilibria. These nonhydrodynamic excitations are known to structurally differ between weakly and strongly coupled quantum field theories with no known results at intermediate values of the interaction strength. We demonstrate that all the known behaviors of transient excitations can be understood as a consequence of different realizations of a symmetry principle, the shift symmetry, applied at the level of the far-from-equilibrium generalization of the hydrodynamic effective action that we explicitly construct. Our approach naturally includes the effects of stochastic fluctuations outside the hydrodynamic regime and allows to explicitly construct hybrid models interpolating between weak- and strong-coupling behavior. We study properties of one such model motivated by thermalization in nuclear collisions in light of the QCD running coupling.

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Phys. Rev. Lett. 137, 192301– Published 3 November, 2026
  • Received 2 December 2025
  • Revised 4 September 2026
  • Accepted 8 October 2026
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