2+1 dimensional pure YangMills theory: Quark confinement and Dual representation
Abstract
We report some progress on the quark confinement problem in 2+1 dim. pure YangMills theory, using Euclidean instanton methods. The instantons are regularized WuYang 'monopoles', whose long range Coulomb field is screened by collective effects. Such configurations are stable to small perturbations unlike the case of singular, undressed monopoles. Using exact nonperturbative results for the 3dim. Coulomb gas, where Debye screening holds for arbitrarily low temperatures, we show in a selfconsistent way that a mass gap is dynamically generated in the gauge theory. The mass gap also determines the size of the monopoles. We also identify the disorder operator of the model in terms of the sineGordon field of the Coulomb gas and hence obtain a dual representation whose symmetry is the centre of SU(2).
 Publication:

Nuclear Physics B Proceedings Supplements
 Pub Date:
 February 1996
 DOI:
 10.1016/09205632(95)006397
 Bibcode:
 1996NuPhS..45..217W