Anisotropic shear viscosity of a strongly coupled non-Abelian plasma from magnetic branes

TL;DR

This paper investigates how strong magnetic fields in heavy ion collisions induce anisotropic shear viscosity in a strongly coupled plasma, revealing that viscosity perpendicular to the field saturates the bound while parallel viscosity slightly violates it.

Contribution

It provides the first holographic calculation of anisotropic shear viscosities in a magnetized strongly coupled plasma, showing minimal violation of the viscosity bound.

Findings

Perpendicular shear viscosity saturates the bound $rac{1}{4 ext{pi}}$.

Parallel shear viscosity is below the bound, indicating violation.

Violations are minimal even at high magnetic fields.

Abstract

Recent estimates for the electromagnetic fields produced in the early stages of non-central ultra-relativistic heavy ion collisions indicate the presence of magnetic fields $B\sim \mathcal{O}(0.1-15\,m_\pi^2)$, where $m_\pi$ is the pion mass. It is then of special interest to study the effects of strong (Abelian) magnetic fields on the transport coefficients of strongly coupled non-Abelian plasmas, such as the quark-gluon plasma formed in heavy ion collisions. In this work we study the anisotropy in the shear viscosity induced by an external magnetic field in a strongly coupled $\mathcal{N} = 4$ SYM plasma. Due to the spatial anisotropy created by the magnetic field, the most general viscosity tensor of a magnetized plasma has 5 shear viscosity coefficients and 2 bulk viscosities. We use the holographic correspondence to evaluate two of the shear viscosities, $\eta_{\perp} \equiv \eta_{xyxy}$ (perpendicular to the magnetic field) and $\eta_{\parallel} \equiv \eta_{xzxz}=\eta_{yzyz}$ (parallel to the field). When $B\neq 0$ the shear viscosity perpendicular to the field saturates the viscosity bound $\eta_{\perp}/s = 1/(4\pi)$ while in the direction parallel to the field the bound is violated since $\eta_{\parallel}/s < 1/(4\pi)$. However, the violation of the bound in the case of strongly coupled SYM is minimal even for the largest value of $B$ that can be reached in heavy ion collisions.