Out-of-time-order hydrodynamics and scrambling
Abstract
Hydrodynamics as an effective field theory (EFT) has been immensely successful for predicting the behaviour of time-ordered correlation functions in the long-time, large-distance regime. In this paper, we analyse the predictions of hydrodynamics for scrambling as probed by out-of-time order correlators (OTOCs). To do so, we consider an all-derivative order generalisation of the Schwinger-Keldysh EFT of hydrodynamics extended to a four-fold time contour required to capture OTOCs. A crucial ingredient of the construction is a local SL(2,R) symmetry, which has previously been suggested as a mechanism for scrambling. We also derive this exact EFT from the microscopic formulation of the maximally chaotic low-temperature limit of the SYK lattice, thereby determining all transport coefficients for this model. As a novel application, we compute the OTOC of energy currents, find that its exponential growth saturates the chaos bound, and match it to expectations based on a shockwave (or scramblon) effective description. Our work shows that the universality of hydrodynamics degrees of freedom extends beyond traditional time-ordered correlators to more complex observables such as OTOCs.
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BibTeX
@misc{bucca2026outoftimeorder,
title = {{Out-of-time-order hydrodynamics and scrambling}},
author = {Marta Bucca and Akash Jain and Márk Mezei and Alexey Milekhin},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.16888},
eprint = {2610.16888},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.16888},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Out-of-time-order hydrodynamics and scrambling
AU - Marta Bucca
AU - Akash Jain
AU - Márk Mezei
AU - Alexey Milekhin
PY - 2026
DA - 2026/10/12
PB - arXiv
DO - 10.48550/arxiv.2610.16888
UR - https://arxiv.org/abs/2610.16888
AB - Hydrodynamics as an effective field theory (EFT) has been immensely successful for predicting the behaviour of time-ordered correlation functions in the long-time, large-distance regime. In this paper, we analyse the predictions of hydrodynamics for scrambling as probed by out-of-time order correlators (OTOCs). To do so, we consider an all-derivative order generalisation of the Schwinger-Keldysh EFT of hydrodynamics extended to a four-fold time contour required to capture OTOCs. A crucial ingredient of the construction is a local SL(2,R) symmetry, which has previously been suggested as a mechanism for scrambling. We also derive this exact EFT from the microscopic formulation of the maximally chaotic low-temperature limit of the SYK lattice, thereby determining all transport coefficients for this model. As a novel application, we compute the OTOC of energy currents, find that its exponential growth saturates the chaos bound, and match it to expectations based on a shockwave (or scramblon) effective description. Our work shows that the universality of hydrodynamics degrees of freedom extends beyond traditional time-ordered correlators to more complex observables such as OTOCs.
ER -