String Tension and Chern-Simons Fluctuations in the Vortex Vacuum of d=3 Gauge Theory

Abstract

Based on a model of the d=3 SU(2) pure gauge theory vacuum as a monopole-vortex condensate, we give a quantitative (if model-dependent) estimate of the relation between the string tension and a gauge-invariant measure of the Chern-Simons susceptibility, due to vortex linkages, in the absence of a Chern-Simons term in the action. We also give relations among these quantities and the vacuum energy and gauge-boson mass. Both the susceptibility and the string tension come from the same physics: The topology of linking, twisting, and writhing of closed vortex strings. The closed-vortex string is described via a complex scalar field theory whose action has a precisely-specified functional form, inferred from previous work giving the exact form of a gauge-theory effective potential at low momentum. Applications to high-T phenomena, including B+L anomalous violation, are mentioned.