Abstract
We report some progress on the quark confinement problem in 2 + 1 dim. pure Yang-Mills theory, using Euclidean instanton methods. The instantons are regularized Wu-Yang ‘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 non-perturbative results for the 3-dim. Coulomb gas, where Debye screening holds for arbitrarily low temperatures, we show in a self-consistent 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 Sine-Gordon field of the Coulomb gas and hence obtain a dual representation whose symmetry is the centre ofSU(2).
Similar content being viewed by others
References
S R Das and S R Wadia,Phys. Rev. D53, 5856 (1996)
A M Polyakov,Nucl. Phys. B120, 429 (1977)
S R Wadia and S R Das,Phys. Lett. B106, 386 (1981)
G ’t Hooft,Nucl. Phys. B190, [FS3], 455 (1981)
T T Wu and C N Yang, inProperties of matter under unusual conditions edited by H Mark and S Fernback (New York, 1969)
T Banks, R Myerson and J Kogut,Nucl. Phys. B129, 493 (1977)
C Callan, R Dashen and D Gross,Phys. Lett. B63, 334 (1976)
D C Brydges,Comm. Math. Phys. 58, 313 (1978)
D C Brydges and P Federbush,Comm. Math. Phys. 73, 197 (1980)
T Yoneya,Phys. Rev. D8, 2567 (1977)
G ’t Hooft,Nucl. Phys. B138, 1 (1978);Nucl. Phys. B153, 141 (1979)
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Wadia, S.R. Quark confinement in 2+1 dimensional pure Yang-Mills theory. Pramana - J Phys 49, 71–80 (1997). https://doi.org/10.1007/BF02856339
Issue Date:
DOI: https://doi.org/10.1007/BF02856339