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The proof uses beautiful physical intuition about the dynamics of nonabelian gauge theories in two dimensions.
What is String Theory Good For (Part I)? « Imaginary Potential

This has been done so far only for gauge group U (1); the nonabelian cases remain.

The “funny region”  where time and space have no meaning  is handled (via a “dual” or “indirect” description) by a particular type of nonabelian gauge theory (for the nonexpert: roughly the same sort of theory that, for example, describes how nuclei hold themselves together) which does not seem particularly exotic, despite the novel spacetime physics it allows them to get a handle on.

It has so far only been done for gauge group U (1); there is a partial result for U (1) X SU (2) but the general nonabelian case remains … A couple of places to look for more details would be hepth/0102028 and heplat/0009033.

Politzer and Frank Wilczek simultaneously found that for a nonabelian gauge field theory the requirement of asymptotic freedom is satisfied if there are not too many quarks.

The success of nonabelian gauge theories showed that all the interactions could be unified in a common framework.

The discovery of asymptotic freedom opened up for a nonabelian gauge field theory for the interactions among quarks and it was called QuantumChromodynamics,

The nonabelian gauge theory of electroweak interaction had become a functioning theoretic machinery and it was possible, just as it had become for quantum electrodynamics 20 years previously, to start performing precise calculations.

As opposed to the abelian variant, in which gauge transformations can be performed in any order, the result of the nonabelian depends on the order.

His task was to help in the search for a method of renormalizing nonabelian gauge theories. 't
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