# Effective field theory of dissipative fluids

## Abstract

We develop an effctive fi eld theory for dissipative fluids which governs the dynamics of long-lived gapless modes associated with conserved quantities. The resulting theory gives a path integral formulation of fluctuating hydrodynamics which systematically incorporates nonlinear interactions of noises. The dynamical variables are mappings between a "fluid spacetime" and the physical spacetime and an essential aspect of our formulation is to identify the appropriate symmetries in the fluid spacetime. The theory applies to nonlinear disturbances around a general density matrix. For a thermal density matrix, we require an additional Z2 symmetry, to which we refer as the local KMS condition. This leads to the standard constraints of hydrodynamics, as well as a nonlinear generalization of the Onsager relations. It also leads to an emergent supersymmetry in the classical statistical regime, and a higher derivative deformation of supersymmetry in the full quantum regime.

- Authors:

- Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)

- Publication Date:

- Research Org.:
- Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)

- Sponsoring Org.:
- USDOE

- OSTI Identifier:
- 1429916

- Grant/Contract Number:
- FG02-05ER41360

- Resource Type:
- Journal Article: Accepted Manuscript

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

- Additional Journal Information:
- Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2017; Journal Issue: 9; 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, Space-Time Symmetries, Quantum Dissipative Systems, Supersymmetric Effective Theories

### Citation Formats

```
Crossley, Michael, Glorioso, Paolo, and Liu, Hong.
```*Effective field theory of dissipative fluids*. United States: N. p., 2017.
Web. doi:10.1007/JHEP09(2017)095.

```
Crossley, Michael, Glorioso, Paolo, & Liu, Hong.
```*Effective field theory of dissipative fluids*. United States. doi:10.1007/JHEP09(2017)095.

```
Crossley, Michael, Glorioso, Paolo, and Liu, Hong. Wed .
"Effective field theory of dissipative fluids". United States.
doi:10.1007/JHEP09(2017)095. https://www.osti.gov/servlets/purl/1429916.
```

```
@article{osti_1429916,
```

title = {Effective field theory of dissipative fluids},

author = {Crossley, Michael and Glorioso, Paolo and Liu, Hong},

abstractNote = {We develop an effctive fi eld theory for dissipative fluids which governs the dynamics of long-lived gapless modes associated with conserved quantities. The resulting theory gives a path integral formulation of fluctuating hydrodynamics which systematically incorporates nonlinear interactions of noises. The dynamical variables are mappings between a "fluid spacetime" and the physical spacetime and an essential aspect of our formulation is to identify the appropriate symmetries in the fluid spacetime. The theory applies to nonlinear disturbances around a general density matrix. For a thermal density matrix, we require an additional Z2 symmetry, to which we refer as the local KMS condition. This leads to the standard constraints of hydrodynamics, as well as a nonlinear generalization of the Onsager relations. It also leads to an emergent supersymmetry in the classical statistical regime, and a higher derivative deformation of supersymmetry in the full quantum regime.},

doi = {10.1007/JHEP09(2017)095},

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

number = 9,

volume = 2017,

place = {United States},

year = {Wed Sep 20 00:00:00 EDT 2017},

month = {Wed Sep 20 00:00:00 EDT 2017}

}

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