Magnetic field-induced gluonic (inverse) catalysis and pressure (an)isotropy in QCD

We study the influence of strong external magnetic fields on gluonic and fermionic observables in the QCD vacuum at zero and nonzero temperatures, via lattice simulations with N_f=1+1+1 staggered quarks of physical masses. The gluonic action density is found to undergo magnetic catalysis at low temperatures and inverse magnetic catalysis near and above the transition temperature, similar to the quark condensate. Moreover, the gluonic action develops an anisotropy: the chromo-magnetic field parallel to the external field is enhanced, while the chromo-electric field in this direction is suppressed. We demonstrate that the same hierarchy is obtained using the Euler-Heisenberg effective action. Conversely, the topological charge density correlator does not reveal a significant anisotropy up to magnetic fields eB~1 GeV^2. Furthermore, we show that the pressure remains isotropic even for nonzero magnetic fields, if it is defined through a compression of the system at fixed external field. In contrast, if the flux of the field is kept fixed during the compression -- which is the situation realized in the lattice simulation -- the pressure develops an anisotropy. We estimate the quark and gluonic contributions to this anisotropy, and relate them to the magnetization of the QCD vacuum. After performing electric charge renormalization, we obtain an estimate for the magnetization, which indicates that QCD is paramagnetic.