Magnetising the $\mathcal{N}=4$ Super Yang-Mills plasma

Abstract

We investigate the thermodynamics of the anisotropic magnetic $\mathrm{Ad}{\mathrm{S}}_5$ black brane solution found by D'Hoker and Kraus arXiv:0908.3875. This solution is the gravity dual of a strongly coupled $\mathcal{N}=4$ Super Yang-Mills plasma in ${\mathbb{R}}^{3,1}$, with temperature $T$, in the presence of a magnetic field $\mathcal{B}$. Following the procedure of holographic renormalisation we calculate the Gibbs free energy and the holographic stress tensor of the conformal plasma. We evaluate several thermodynamic quantities including the magnetisation, the anisotropic pressures and the speeds of sound. Our results are consistent with an RG flow from a perturbed $\mathrm{Ad}{\mathrm{S}}_5$ black brane at small $\mathcal{B}/T^2$ to a $\mathbf{BTZ}\times {\mathbb{R}}^2$ black brane at large $\mathcal{B}/T^2$. We also perform a phenomenological analysis where we compare the thermodynamics of a magnetised conformal plasma against the lattice QCD results for the thermodynamics of the magnetised quark-gluon plasma.

arXiv commentV1 40 pages, 11 figures. V2 42 pages, 11 figures, references added. New subsection about the non-diffeomorphism invariant counterterm and the conformal anomaly. V3 44 pages, 12 figures, accepted in JHEP

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• Inverse magnetic catalysis and energy loss in holographic QCD model
• Magnetized AdS/BCFT Correspondence in Horndeski Gravity
• Interplay of magnetic field and chemical potential induced anisotropy and frame dependent chaos of a $Q\bar{Q}$ pair in holographic QCD
• Probing Quarkonium Diffusion in a Magnetized Quark-Gluon Plasma
• Complexity of Magnetization and Magnetic Simplification