Emergent Supersymmetry in Local Equilibrium Systems

TL;DR

The paper shows that any classical statistical system in local thermal equilibrium possesses an emergent supersymmetry at low energies, arising from the interplay between BRST symmetry (necessitated by time-evolution unitarity) and a dynamical KMS symmetry. It develops a general non-equilibrium EFT framework on the closed time path, proves a supersymmetrizability theorem for bosonic actions satisfying a special dynamical KMS condition, and constructs explicit SUSY-formulated theories for Model A, nonlinear diffusion, and fluctuating hydrodynamics. The results provide a unified symmetry perspective on fluctuations in non-equilibrium steady states and furnish concrete supersymmetric formulations that include ghost sectors, improving control over loop effects and transport phenomena. This framework paves the way for systematic analyses of fluctuations, transport coefficients, and potential fixed points in far-from-equilibrium dynamics, with quantum extensions remaining an open frontier.

Abstract

Many physical processes we observe in nature involve variations of macroscopic quantities over spatial and temporal scales much larger than microscopic molecular collision scales and can be considered as in local thermal equilibrium. In this paper we show that any classical statistical system in local thermal equilibrium has an emergent supersymmetry at low energies. We use the framework of non-equilibrium effective field theory for quantum many-body systems defined on a closed time path contour and consider its classical limit. Unitarity of time evolution requires introducing anti-commuting degrees of freedom and BRST symmetry which survive in the classical limit. The local equilibrium is realized through a $Z_2$ dynamical KMS symmetry. We show that supersymmetry is equivalent to the combination of BRST and a specific consequence of the dynamical KMS symmetry, to which we refer as the special dynamical KMS condition. In particular, we prove a theorem stating that a system satisfying the special dynamical KMS condition is always supersymmetrizable. We discuss a number of examples explicitly, including model A for dynamical critical phenomena, a hydrodynamic theory of nonlinear diffusion, and fluctuating hydrodynamics for relativistic charged fluids.