Magnetic field effects on the static quark potential at zero and finite temperature

We investigate the static QQ potential at zero and finite temperature in the presence of a constant and uniform external magnetic field (B) over right arrow, for several values of the lattice spacing and for different orientations with respect to (B) over right arrow. As a byproduct, we provide continuum limit extrapolated results for the string tension, the Coulomb coupling and the Sommer parameter at T = 0 and B = 0. We confirm the presence in the continuum of a B-induced anisotropy, regarding essentially the string tension, for which it is of the order of 15% at vertical bar e vertical bar B similar to 1 GeV2 and would suggest, if extrapolated to larger fields, a vanishing string tension along the magnetic field for vertical bar e vertical bar B greater than or similar to 4 GeV2. The angular dependence for vertical bar e vertical bar B less than or similar to 1 GeV2 can be nicely parametrized by the first allowed term in an angular Fourier expansion, corresponding to a quadrupole deformation. Finally, for T not equal 0, the main effect of the magnetic field is a general suppression of the string tension, leading to a early loss of the confining properties: this happens even before the appearance of inverse magnetic catalysis in the chiral condensate, supporting the idea that the influence of the magnetic field on the confining properties is the leading effect originating the decrease of T-c as a function of B.