Shear mode transport coefficients from multiple polylogarithms

TL;DR

This paper analytically computes shear transport coefficients in AdS black branes using multiple polylogarithms, extending previous results for $ ext{N}=4$ SYM to higher orders and dimensions.

Contribution

It introduces a method to express shear transport coefficients in terms of multiple polylogarithms and extends calculations to higher orders and dimensions.

Findings

Computed shear transport coefficients for $ ext{N}=4$ SYM up to order $ ext{q}^{10}$.

Generalized the computation method to $d+1$ dimensions.

Characterized the mathematical structure of the resulting expressions.

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 transport coefficients for $\mathcal{N}=4$ SYM, by performing a bulk computation in the five-dimensional black hole background up to order $\mathfrak{q}^{10}$, which extends the results previously available in the literature. We then generalise the procedure to $d+1$ dimensions, characterising the mathematical structure of the resulting transport coefficient expressions.