Abstract
We study the behaviour of holographic entanglement entropy (HEE) in near equilibrium thermal states which are macroscopically described by conformal relativistic hydrodynamic flows dual to dynamical black brane geometries. We compute HEE for strip-shaped subsystems in boundary dimensions d = 2, 3, 4, which provides us with general qualitative inferences on the interplay between fluid flows and entanglement dynamics. At first, we consider the zeroth order in hydrodynamic derivative expansion, holographically described by stationary boosted black branes. Working non-perturbatively in fluid velocity, we find that, as the fluid velocity approaches its relativistic upper limit, the UV regulated HEE exhibits a divergence at arbitrary temperature. Also, the holographic mutual information between two relatively close subsystems vanishes at some critical fluid velocity and remains zero beyond it. We then compute HEE in an excited state of the fluid in the presence of the sound mode. As a simplified setup, we first work with non-dissipative dynamics in d = 2, where the time evolution of HEE is studied in the presence of the sound mode and a propagating pressure pulse. In d = 4, working upto first order in derivative expansion, we find that dissipative sound modes produce an additional dynamical UV divergence which is subleading compared to the ‘area law divergence’. No such divergence is observed for dissipative sound mode in d = 3.
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Acknowledgments
We would like to thank Anirudh Deb for initial collaboration and many useful discussions. We are also particularly grateful to Anirban Dinda and Nilakash Sorokhaibam for many insightful discussions. We would also like to thank Sayantani Bhattacharyya, Diptarka Das, Bobby Ezhuthachan, Sayan Kar, Apratim Kaviraj, S. Pratik Khastgir, Arnab Kundu, Nilay Kundu, R. Loganayagam, Sabyasachi Maulik, Kannabiran Seshasayanan, Vishwanath Shukla for several useful discussions. We are also extremely thankful to Shankhadeep Chakrabortty, Anirudh Deb and Tadashi Takayanagi for their valuable comments on the draft of our paper. JB and SKD would like to acknowledge hospitality at NISER Bhubaneshwar, during the workshop titled ‘Regional strings meeting 2022’, where some of the results reported in this paper were first presented. PB would like to acknowledge hospitality at IIT Kharagpur during the course of this work. JB would like to acknowledge support from the Institute Scheme for Innovative Research and Development (ISIRD), IIT Kharagpur, Grant No. IIT/SRIC/PH/RFL/2021-2022/091. PB would like to acknowledge the support provided by the grant CRG/2021/004539.
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ArXiv ePrint: 2211.14271
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Bhattacharya, J., Biswas, P., Chandranathan, A. et al. Holographic entanglement entropy for relativistic hydrodynamic flows. J. High Energ. Phys. 2023, 92 (2023). https://doi.org/10.1007/JHEP05(2023)092
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DOI: https://doi.org/10.1007/JHEP05(2023)092