Three-dimensional Yang-Mills Theory Research Articles

Dynamical mass generation in three-dimensional Yang-Mills theory

We calculate an effective potential for three-dimensional Yang-Mills theory to two loops. The result implies that a gauge invariant part of the field strength has a non-zero vacuum expectation value, φ. The two-point function of this field, calculated to one loop, shows that two polarization states propagate with a mass proportional to √ φ. In contrast to the usual Higgs mechanism the remaining degrees of freedom do not propagate. This dynamical generation of a “glueball” mass renders the already ultraviolet finite theory infrared finite and stabilizes vortices associated with the centre of the group.

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 ${T}^{\frac{1}{2}}g(T)$. This implies that the leading-order magnetostatic mass gap must be proportional to ${g}^{2}T$.

Perturbative results on QCD 3 at finite temperature

Three-dimensional Yang-Mills theory is analyzed at finite temperature using perturbation theory. It is shown that all infrared divergences can be eliminated by introducing a self-consistent electric mass that is gauge invariant to all orders in perturbation theory. The dependence of the electric mass on temperature and coupling constant is non-analytic, and is shown to be calculable order by order in perturbation theory. Its behavior suggests the existence of a second-order phase transition by which the quark free energy becomes divergent, in agreement with Monte Carlo calculations. The magnetic mass and the lowest order correction to the spacelike string tension are computed. We argue that the Wilson string decouples at the critical point.