Deconfinement and chiral symmetry restoration in a strong magnetic background

We perform a model study of deconfinement and chiral symmetry restoration in a strong magnetic background. We use a Nambu-Jona-Lasinio model with the Polyakov loop, taking into account a possible dependence of the coupling on the Polyakov-loop expectation value, as suggested by the recent literature. Our main result is that, within this model, the deconfinement and chiral crossovers of QCD in strong magnetic field are entangled even at the largest value of eB considered here, namely eB = 30m(pi)(2) (that is, B approximate to 6 X 10(15) T). The amount of split that we measure is, at this value of eB, of the order of 2%. We also study briefly the role of the 8-quark term on the entanglement of the two crossovers. We then compare the phase diagram of this model with previous results, as well as with available lattice data.