Quark deconfinement and gluon condensate in a weak magnetic field from QCD sum rules

We study QCD finite energy sum rules (FESR) for the axial-vector current correlator in the presence of a magnetic field, in the weak field limit and at zero temperature. We find that the perturbative QCD and the hadronic contribution to the sum rules get explicit magnetic-field-dependent corrections and that these in turn induce a magnetic field dependence on the deconfinement phenomenological parameter s(0) and on the gluon condensate. The leading corrections turn out to be quadratic in the field strength. We find from the dimension d = 2 first FESR that the magnetic field dependence of s(0) is proportional to the absolute value of the light-quark condensate. Hence, it increases with increasing field strength. This implies that the parameters describing chiral symmetry restoration and deconfinement behave similarly as functions of the magnetic filed. Thus, at zero temperature the magnetic field is a catalyzing agent of both chiral symmetry breaking and confinement. From the dimension d = 4 second FESR we obtain the behavior of the gluon condensate in the presence of the external magnetic field. This condensate also increases with increasing field strength.