U(1) quasi-hydrodynamics: Schwinger-Keldysh effective field theory and holography

Matteo Baggioli (Wilczek Quantum Center, School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai, 200240, China; Shanghai Research Center for Quantum Sciences, Shanghai, 201315, China) ; Yanyan Bu (School of Physics, Harbin Institute of Technology, Harbin, 150001, China) ; Vaios Ziogas (CPHT, CNRS, École polytechnique, Institut Polytechnique de Paris, Palaiseau, 91120, France)

We study the quasi-hydrodynamics of a system with a softly broken U(1) global symmetry using effective field theory (EFT) and holographic methods. In the gravity side, we consider a holographic Proca model in the limit of small bulk mass, which is responsible for a controllable explicit breaking of the U(1) global symmetry in the boundary field theory. We perform a holographic Schwinger-Keldysh analysis, which allows us to derive the form of the boundary effective action in presence of dissipation. We compare our results with the previously proposed EFT and hydrodynamic theories, and we confirm their validity by computing the low-energy quasi-normal modes spectrum analytically and numerically. Additionally, we derive the broken holographic Ward identity for the U(1) current, and discuss the recently proposed novel transport coefficients for systems with explicitly broken symmetries. The setup considered is expected to serve as a toy model for more realistic situations where quasi-hydrodynamics is at work, such as axial charge relaxation in QCD, spin relaxation in relativistic systems, electric field relaxation in magneto-hydrodynamics, or momentum relaxation in condensed matter systems.

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      "surname": "Bu", 
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      "value": "We study the quasi-hydrodynamics of a system with a softly broken U(1) global symmetry using effective field theory (EFT) and holographic methods. In the gravity side, we consider a holographic Proca model in the limit of small bulk mass, which is responsible for a controllable explicit breaking of the U(1) global symmetry in the boundary field theory. We perform a holographic Schwinger-Keldysh analysis, which allows us to derive the form of the boundary effective action in presence of dissipation. We compare our results with the previously proposed EFT and hydrodynamic theories, and we confirm their validity by computing the low-energy quasi-normal modes spectrum analytically and numerically. Additionally, we derive the broken holographic Ward identity for the U(1) current, and discuss the recently proposed novel transport coefficients for systems with explicitly broken symmetries. The setup considered is expected to serve as a toy model for more realistic situations where quasi-hydrodynamics is at work, such as axial charge relaxation in QCD, spin relaxation in relativistic systems, electric field relaxation in magneto-hydrodynamics, or momentum relaxation in condensed matter systems."
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Published on:
04 September 2023
Publisher:
Springer
Published in:
Journal of High Energy Physics , Volume 2023 (2023)
Issue 9
Pages 1-45
DOI:
https://doi.org/10.1007/JHEP09(2023)019
arXiv:
2304.14173
Copyrights:
The Author(s)
Licence:
CC-BY-4.0

Fulltext files: