Shear Viscosity from AdS Born-Infeld Black Holes

TL;DR

This work investigates whether nonlinear gauge-field (Born-Infeld) corrections in Einstein-Born-Infeld gravity alter the shear viscosity to entropy density ratio $η/s$ of the dual field theory in the AdS/CFT framework. Using the AdS Born-Infeld black hole background and the Kubo formula with tensor perturbations, the authors expand to first order in the Born-Infeld parameter $1/b^2$ and compute the retarded Green's function, obtaining $η = (1/(16π G))(r_+^3 / l^3)$ and $s = (1/(4G))(r_+^3 / l^3)$, which yields $η/s = 1/(4π)$. They further show that higher-derivative corrections to the gauge field, effectively shifting $1/b^2$ to $1/b^2+4c$, do not modify the ratio at this order, while corrections to gravity can. The results support the view that the universality of $η/s = 1/(4π)$ is governed by the gravity sector in the dual description, with gauge-field higher-derivative terms leaving the ratio invariant at leading nontrivial order.

Abstract

We calculate the shear viscosity in the frame of AdS/CFT correspondence for the field theory with a gravity dual of Einstein-Born-Infeld gravity. We find that the ratio of $η/s$ is still the conjectured universal value $1/4π$ at least up to the first order of the Born-Infeld parameter $1/b^2$.