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  • Open Access

Shear mode transport coefficients from multiple polylogarithms

Paolo Arnaudo*

  • *Contact author: p.arnaudo@soton.ac.uk
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Phys. Rev. D 113, 126011 – Published 8 June, 2026

DOI: https://doi.org/10.1103/db8h-1slc

Abstract

We present an analytical study of the transport coefficients associated with the shear sector of gravitational perturbations around asymptotically anti–de Sitter black branes. In the long-wavelength, low-frequency limit, the wave solutions admit a structure that is fully described in terms of multiple polylogarithms in several variables. We focus primarily on computing the coefficients of the dispersion relation for N=4 super Yang-Mills theory, by performing a bulk computation in the five-dimensional black hole background up to order q10, which extends the results previously available in the literature. We then generalize the procedure to d+1 dimensions, characterizing the mathematical structure of the resulting transport coefficient expressions.

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Phys. Rev. D 113, 126011– Published 8 June, 2026
  • Received 31 March 2026
  • Accepted 30 April 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.

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