Anisotropic shear viscosity of a strongly coupled non-Abelian plasma from magnetic branes
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 o...
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Veröffentlicht in: | arXiv.org 2014-09 |
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Sprache: | eng |
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Zusammenfassung: | 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. |
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ISSN: | 2331-8422 |
DOI: | 10.48550/arxiv.1406.6019 |