Phase diagram of QCD in a magnetic background

Abstract: We provide numerical evidence that the thermal QCD crossover turns into a first order transition in the presence of large enough magnetic background fields. The critical endpoint is found to be located between $eB = 4$ GeV$^2$ (where the pseudocritical temperature is $T_c = (98 \pm 3)$ MeV) and $eB = 9$ GeV$^2$ (where the critical temperature is $T_c = (63 \pm 5)$ MeV). Results are based on the analysis of quark condensates and number susceptibilities, determined by lattice simulations of $N_f = 2+1$ QCD at the physical point, discretized with three different lattice spacings, $a = 0.114, 0.086$ and $0.057$ fm, via rooted stout staggered fermions and a Symanzik tree level improved pure gauge action. We also present preliminary results regarding the confining properties of the thermal theory, suggesting that they could change drastically going across the phase transition