Calculating non-perturbative quantities through the world-line formalism

Abstract

Abstract We present two applications of the world-line formalism to the calculation of non-perturbative quantities in QCD. The first quantity is the free energy of the gluon plasma in the high-temperature limit; the second quantity is the pair-production rate in the chromo-electric field of a flux tube. In the first case, where effects of spatial confinement in the dimensionally-reduced 3D Yang-Mills theory are primarily important, we calculate the free-energy density of a gluon propagating in the stochastic background fields through a suitable parametrization of the area-and the perimeter laws of the Wilson loop, which enters the corresponding one-loop effective action. In this way, we find that the order of the leading correction to the Stefan-Boltzmann free energy changes from O ( λ ) for N ∼ 1 to O ( λ 3 / 2 ) for N ≫ 1, where λ is the finite-temperature’t Hooft coupling, and N is the number of colors. In the second case, we find that, in the London limit of the dual superconductor, the Schwinger pair-production rate, ∼ e−const·m 2, goes over to e−const·m . Given that the flux-tube field is static, we find such a conversion of the Gaussian distribution into an exponential one, remarkable.