Shear viscosity from complex light-cone expansion
Abstract
Near thermal equilibrium, the transverse momentum density in a fluid diffuses according to ω(k) ∼ − i cal D k2 at small k, where the diffusion coefficient cal D is proportional to the shear viscosity. In field theories with a holographic dual description in terms of classical gravity, the shear-mode frequency ω(k) approaches the light cone at large imaginary wave vector. We develop a WKB approach to study this limit. For black branes in AdSp+2, we determine the leading terms of the asymptotic large-k expansion of the shear-mode frequency ω(k). In the case of AdS5, we compute a large number of terms of this series and use resummation techniques to analytically continue the result to small k. We find strong evidence that ω(k) is analytic at k=0 and vanishes there, which amounts to the existence of hydrodynamics encoded in the large-k physics. Taking 10 terms in the large-k expansion of ω(k) gives an answer for cal D which is accurate to better than 0.5%.
Related
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BibTeX
@misc{aniceto2026shear,
title = {{Shear viscosity from complex light-cone expansion}},
author = {Inês Aniceto and Pavel Kovtun and Alex Ratcliffe and Michał Spaliński},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.32892},
eprint = {2610.32892},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.32892},
}
RIS
TY - UNPB
TI - Shear viscosity from complex light-cone expansion
AU - Inês Aniceto
AU - Pavel Kovtun
AU - Alex Ratcliffe
AU - Michał Spaliński
PY - 2026
DA - 2026/10/23
PB - arXiv
DO - 10.48550/arxiv.2610.32892
UR - https://arxiv.org/abs/2610.32892
AB - Near thermal equilibrium, the transverse momentum density in a fluid diffuses according to ω(k) ∼ − i cal D k^2 at small k, where the diffusion coefficient cal D is proportional to the shear viscosity. In field theories with a holographic dual description in terms of classical gravity, the shear-mode frequency ω(k) approaches the light cone at large imaginary wave vector. We develop a WKB approach to study this limit. For black branes in AdS_p+2, we determine the leading terms of the asymptotic large-k expansion of the shear-mode frequency ω(k). In the case of AdS_5, we compute a large number of terms of this series and use resummation techniques to analytically continue the result to small k. We find strong evidence that ω(k) is analytic at k=0 and vanishes there, which amounts to the existence of hydrodynamics encoded in the large-k physics. Taking 10 terms in the large-k expansion of ω(k) gives an answer for cal D which is accurate to better than 0.5%.
ER -