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

We investigate the thermodynamics of anisotropic magnetic $\rm AdS_5$ black brane solution found by D'Hoker and Kraus arXiv:0908.3875. This is gravity dual a strongly coupled ${\cal N}=4$ Super Yang-Mills plasma in ${\mathbb R}^{3,1}$, with temperature $T$, presence field B}$. Following procedure holographic renormalisation we calculate Gibbs free energy stress tensor conformal plasma. evaluate several thermodynamic quantities including magnetisation, pressures speeds sound. Our results are consistent an RG flow from perturbed at small B}/T^2$ to \bf BTZ \times {\mathbb R}^2$ large B}/T^2$. also perform phenomenological analysis where compare magnetised against lattice QCD for quark-gluon