## Emergent supersymmetry in local equilibrium systems

## 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 Z2 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. Here, 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.

- Authors:

- Harvard Univ., Cambridge, MA (United States). Center for the Fundamental Laws of Nature
- Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States). Center for Theoretical Physics

- Publication Date:

- Research Org.:
- Massachusetts Inst. of Tech., Cambridge (United States)

- Sponsoring Org.:
- USDOE

- OSTI Identifier:
- 1507704

- Grant/Contract Number:
- FG02-05ER41360

- Resource Type:
- Accepted Manuscript

- Journal Name:
- Journal of High Energy Physics (Online)

- Additional Journal Information:
- Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2018; Journal Issue: 1; Journal ID: ISSN 1029-8479

- Publisher:
- Springer Berlin

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Effective Field Theories; Quantum Dissipative Systems; Supersymmetric Effective Theories

### Citation Formats

```
Gao, Ping, and Liu, Hong. Emergent supersymmetry in local equilibrium systems. United States: N. p., 2018.
Web. doi:10.1007/jhep01(2018)040.
```

```
Gao, Ping, & Liu, Hong. Emergent supersymmetry in local equilibrium systems. United States. doi:10.1007/jhep01(2018)040.
```

```
Gao, Ping, and Liu, Hong. Wed .
"Emergent supersymmetry in local equilibrium systems". United States. doi:10.1007/jhep01(2018)040. https://www.osti.gov/servlets/purl/1507704.
```

```
@article{osti_1507704,
```

title = {Emergent supersymmetry in local equilibrium systems},

author = {Gao, Ping and Liu, Hong},

abstractNote = {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 Z2 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. Here, 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.},

doi = {10.1007/jhep01(2018)040},

journal = {Journal of High Energy Physics (Online)},

number = 1,

volume = 2018,

place = {United States},

year = {2018},

month = {1}

}