Abstract
We construct stable and causal effective field theories (EFTs) for describing statistical fluctuations in relativistic diffusion and relativistic hydrodynamics. These EFTs are fully non-linear, including couplings to background sources, and enable us to compute n-point time-ordered correlation functions including the effects of statistical fluctuations. The EFTs we construct are inspired by the Maxwell-Cattaneo model of relativistic diffusion and Müller-Israel-Stewart model of relativistic hydrodynamics respectively, and have been derived using both the Martin-Siggia-Rose and Schwinger-Keldysh formalisms. The EFTs non-linearly realise the dynamical Kubo-Martin-Schwinger (KMS) symmetry, which ensures that n-point correlation functions and interactions in the theory satisfy the appropriate fluctuation-dissipation theorems. Since these EFTs typically admit ultraviolet sectors that are not fixed by the low-energy infrared symmetries, we find that they simultaneously admit multiple realisations of the dynamical KMS symmetry. We also comment on certain obstructions to including statistical fluctuations in the recently-proposed stable and causal Bemfica-Disconzi-Noronha-Kovtun model of relativistic hydrodynamics.
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Acknowledgments
We would like to thank N. Abbasi, G. Denicol, M. Hippert, M. Kaminski, and J. Noronha for various useful discussions. We are also thankful to the authors of [48] for sharing a draft of their paper prior to submission. AJ is funded by the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement NonEqbSK No. 101027527. AJ are partly supported by the Netherlands Organization for Scientific Research (NWO) and by the Dutch Institute for Emergent Phenomena (DIEP) cluster at the University of Amsterdam. PK is supported in part by the NSERC of Canada. This project was initiated during “The Many Faces of Relativistic Fluid Dynamics” program at KITP, Santa Barbara, supported by the National Science Foundation under Grant No. NSF PHY-1748958.
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Jain, A., Kovtun, P. Schwinger-Keldysh effective field theory for stable and causal relativistic hydrodynamics. J. High Energ. Phys. 2024, 162 (2024). https://doi.org/10.1007/JHEP01(2024)162
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DOI: https://doi.org/10.1007/JHEP01(2024)162