TY - JOUR

T1 - Anisotropic shear viscosity of a strongly coupled non-Abelian plasma from magnetic branes

AU - Critelli, R.

AU - Finazzo, S. I.

AU - Zaniboni, M.

AU - Noronha, J.

N1 - Publisher Copyright:
© 2014 American Physical Society.

PY - 2014/9/9

Y1 - 2014/9/9

N2 - Recent estimates for the electromagnetic fields produced in the early stages of noncentral ultrarelativistic heavy ion collisions indicate the presence of magnetic fields B∼O(0.1-15mπ2), where mπ 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 paper we study the anisotropy in the shear viscosity induced by an external magnetic field in a strongly coupled N=4 super Yang-Mills (SYM) plasma. Due to the spatial anisotropy created by the magnetic field, the most general viscosity tensor of a magnetized plasma has five shear viscosity coefficients and two bulk viscosities. We use the holographic correspondence to evaluate two of the shear viscosities, η≡ηxyxy (perpendicular to the magnetic field) and η≡ηxzxz=ηyzyz (parallel to the field). When B≠0 the shear viscosity perpendicular to the field saturates the viscosity bound η/s=1/(4π), while in the direction parallel to the field the bound is violated since η/s<1/(4π). 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.

AB - Recent estimates for the electromagnetic fields produced in the early stages of noncentral ultrarelativistic heavy ion collisions indicate the presence of magnetic fields B∼O(0.1-15mπ2), where mπ 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 paper we study the anisotropy in the shear viscosity induced by an external magnetic field in a strongly coupled N=4 super Yang-Mills (SYM) plasma. Due to the spatial anisotropy created by the magnetic field, the most general viscosity tensor of a magnetized plasma has five shear viscosity coefficients and two bulk viscosities. We use the holographic correspondence to evaluate two of the shear viscosities, η≡ηxyxy (perpendicular to the magnetic field) and η≡ηxzxz=ηyzyz (parallel to the field). When B≠0 the shear viscosity perpendicular to the field saturates the viscosity bound η/s=1/(4π), while in the direction parallel to the field the bound is violated since η/s<1/(4π). 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.

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U2 - 10.1103/PhysRevD.90.066006

DO - 10.1103/PhysRevD.90.066006

M3 - Article

AN - SCOPUS:84985018996

SN - 1550-7998

VL - 90

JO - Physical Review D - Particles, Fields, Gravitation and Cosmology

JF - Physical Review D - Particles, Fields, Gravitation and Cosmology

IS - 6

M1 - 066006

ER -