Dimensional reduction in finite-temperature quantum chromodynamics

The infrared behavior of four-dimensional quantum chromodynamics at finite temperature and chemical potential is examined within the context of perturbation theory. The reduction to an effective three-dimensional theory of the Yang-Mills field coupled to a massive adjoint scalar field is explicitly shown to occur at the one-loop level. A renormalization scheme especially appropriate for the reduction is exhibited. By working in a general Lorentz-covariant gauge, the (well-known) one-loop electrostatic mass is shown to be gauge invariant. Infrared divergences at the two-loop level indicate the need for a nonperturbative treatment of the effective theory; their gauge dependence implies that the naive method for computing the electrostatic mass in covariant gauges is invalid beyond one-loop. Further analysis is carried out in a class of gauges ("static gauges") that are particularly well suited for finite-temperature calculations. The systematic construction of the effective theory is outlined, and performed in a static gauge. At distance scales beyond the electrostatic screening length, pertinent to an investigation of possible magnetostatic screening, the effective theory simplifies further to pure three-dimensional Yang-Mills theory with coupling $T^{\frac{1}{2}}g\left(T\right)\mathrm{}$. This implies that the leading-order magnetostatic mass gap must be proportional to $g^{2}T$.