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

R. Critelli; S. I. Finazzo; M. Zaniboni; J. Noronha

doi:10.1103/PhysRevD.90.066006

paper

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

arXiv:1406.6019 · doi:10.1103/PhysRevD.90.066006

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 $B \sim O (0.1 - 15 m_{π}^{2})$ , where $m_{π}$ 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 $N = 4$ 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, $η_{⊥} \equiv η_{x y x y}$ (perpendicular to the magnetic field) and $η_{∥} \equiv η_{x z x z} = η_{y z y z}$ (parallel to the field). When $B \neq = 0$ the shear viscosity perpendicular to the field saturates the viscosity bound $η_{⊥} / s = 1/ (4 π)$ while in the direction parallel to the field the bound is violated since $η_{∥} / s < 1/ (4 π)$ . 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.

21 pages, 3 figures; updated Appendix and references, published in Phys. Rev. D

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

Abstract

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