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

TL;DR

This paper explores the thermodynamics of a strongly coupled ${ m N}=4$ Super Yang-Mills plasma under a magnetic field using holographic duality, revealing RG flow behavior and comparing with lattice QCD results.

Contribution

It provides a detailed holographic analysis of magnetized ${ m N}=4$ SYM plasma, including thermodynamic quantities and RG flow insights, with comparison to QCD data.

Findings

RG flow from perturbed AdS_5 to BTZ x R^2 black brane at large magnetic field.

Calculated thermodynamic quantities like magnetization and pressures.

Results align with lattice QCD for magnetized quark-gluon plasma.

Abstract

We investigate the thermodynamics of the anisotropic magnetic $\rm AdS_5$ black brane solution found by D'Hoker and Kraus arXiv:0908.3875. This solution is the gravity dual of a strongly coupled ${\cal N}=4$ Super Yang-Mills plasma in ${\mathbb R}^{3,1}$, with temperature $T$, in the presence of a magnetic field ${\cal B}$. 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 $\rm AdS_5$ black brane at small ${\cal B}/T^2$ to a $\rm \bf BTZ \times {\mathbb R}^2$ black brane at large ${\cal B}/T^2$. 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.