Abstract
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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Acknowledgments
We would like to thank Navid Abbasi, Danny Brattan, Aristomenis Donos, Paolo Glorioso, Blaise Goutéraux, Sebastian Grieninger, Michael Landry and Ashish Shukla for useful discussions. We would also like to thank Akash Jain and Jay Armas for discussions on the relation between our results and theirs. M.B. acknowledges the support of the Shanghai Municipal Science and Technology Major Project (Grant No.2019SHZDZX01) and the sponsorship from the Yangyang Development Fund. V.Z. is supported by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation program (grant agreement No758759).
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Baggioli, M., Bu, Y. & Ziogas, V. U(1) quasi-hydrodynamics: Schwinger-Keldysh effective field theory and holography. J. High Energ. Phys. 2023, 19 (2023). https://doi.org/10.1007/JHEP09(2023)019
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DOI: https://doi.org/10.1007/JHEP09(2023)019