Effective action for relativistic hydrodynamics: fluctuations, dissipation, and entropy inflow

Haehl, Felix M.; Loganayagam, R.; Rangamani, Mukund

doi:10.1007/jhep10(2018)194

Title: Effective action for relativistic hydrodynamics: fluctuations, dissipation, and entropy inflow

Journal Article · 30 October 2018 · Journal of High Energy Physics (Online)

DOI: https://doi.org/10.1007/jhep10(2018)194 · OSTI ID:1611306

Haehl, Felix M. ^[1]; Loganayagam, R. ^[2]; Rangamani, Mukund ^[3]

Univ. of British Columbia, Vancouver, BC (Canada). Dept. of Physics and Astronomy; DOE/OSTI
International Centre for Theoretical Sciences (ICTS-TIFR) (India)
Univ. of California, Davis, CA (United States). Dept. of Physics

We present a detailed and self-contained analysis of the universal SchwingerKeldysh effective field theory which describes macroscopic thermal fluctuations of a relativistic field theory, elaborating on our earlier construction. We write an effective action for appropriate hydrodynamic Goldstone modes and fluctuation fields, and discuss the symmetries to be imposed. The constraints imposed by fluctuation-dissipation theorem are manifest in our formalism. Consequently, the action reproduces hydrodynamic constitutive relations consistent with the local second law at all orders in the derivative expansion, and captures the essential elements of the eightfold classification of hydrodynamic transport of. We demonstrate how to recover the hydrodynamic entropy and give predictions for the non-Gaussian hydrodynamic fluctuations. The basic ingredients of our construction involve (i) doubling of degrees of freedom a la Schwinger-Keldysh, (ii) an emergent gauge U(1)_T symmetry associated with entropy which is encapsulated in a Noether current a la Wald, and (iii) a BRST/topological supersymmetry imposing the fluctuation-dissipation theorem a la Parisi-Sourlas. The overarching mathematical framework for our construction is provided by the balanced equivariant cohomology of thermal translations, which captures the basic constraints arising from the Schwinger-Keldysh doubling, and the thermal Kubo-Martin-Schwinger relations. All these features are conveniently implemented in a covariant superspace formalism. An added benefit is that the second law can be understood as being due to entropy inflow from the Grassmann-odd directions of superspace.

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Research Organization:: Univ. of California, Davis, CA (United States)

Sponsoring Organization:: USDOE Office of Science (SC), High Energy Physics (HEP) (SC-25)

Grant/Contract Number:: SC0009999

OSTI ID:: 1611306

Journal Information:: Journal of High Energy Physics (Online), Journal Name: Journal of High Energy Physics (Online) Journal Issue: 10 Vol. 2018; ISSN 1029-8479

Publisher:: Springer BerlinCopyright Statement

Country of Publication:: United States

Language:: English

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