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Alexander Polyakov studied the confinement of Abelian compat U(1) gauge theory without matter field in 1975 at "Compact gauge fields and the infrared catastrophe. Phys.Lett. B59- 82–84 (1975)," see the Abstract:

"It is shown that infrared phenomena in the gauge theories are guided by certain classical solutions of the Yang- Mills equations. The existence of such solutions can lead to a finite correlation length which stops infrared catastrophe. In the present paper we deal only with theories with a compact but abelian gauge group. In this case the problems of correlation length and charge confinement are completely solved."

However, it is mentioned in his Conclusion that "The extension of the above ideas on the nonabelian theory will be presented in the other papers of this series."

I had hard time finding the Refs on the Polyakov's confinement analysis on the nonabelian theory. What are the References?

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Maybe this Quark confinement and topology of gauge theories, Nuclear Physics B Volume 120, Issue 3, 21 March 1977, Pages 429-458. From abstract:

"The phenomenon of quark confinement is known to be connected with the restoration of apparently broken gauge symmetry. In this paper we focus on a special mechanism which is responsible for such restoration... Initially, we demonstrate this mechanism in certain simple non-gauge models... Finally, we turn to the more realistic case of a 3 + 1 dimensional non-Abelian gauge theory."

See also Ch. 5 in Polyakov's book Gauge Fields and Strings, and Vortices and quark confinement in non-Abelian gauge theories, Physics Reports; v. 23(3) (1976) p. 245-249 by Mandelstam.

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