Gravity assisted solution of the mass gap problem for pure Yang-Mills fields

Abstract

In 1979 Louis Witten demonstrated that stationary axially symmetric Einstein field equations and those for static axially symmetric self-dual SU(2) gauge fields can both be reduced to the same (Ernst) equation. In this paper we use this result as point of departure to prove the existence of the mass gap for quantum source-free Yang-Mills (Y-M) fields. The proof is facilitated by results of our recently published paper, JGP 59 (2009) 600-619. Since both pure gravity, the Einstein-Maxwell and pure Y-M fields are described for axially symmetric configurations by the Ernst equation classically, their quantum descriptions are likely to be interrelated. Correctness of this conjecture is successfully checked by reproducing (by different methods) results of Korotkin and Nicolai, Nucl.Phys.B475 (1996) 397-439, on dimensionally reduced quantum gravity. Consequently, numerous new results supporting the Faddeev-Skyrme (F-S) -type models are obtained. We found that the F-S-like model is best suited for description of electroweak interactions while strong interactions require extension of Witten's results to the SU(3) gauge group. Such an extension is nontrivial. It is linked with the symmetry group SU(3)xSU(2)xU(1) of the Standard Model. This result is quite rigid and should be taken into account in development of all grand unified theories. Also, the alternative (to the F-S-like) model emerges as by-product of such an extension. Both models are related to each other via known symmetry transformation. Both models possess gap in their excitation spectrum and are capable of producing knotted/linked configurations of gauge/gravity fields. In addition, the paper discusses relevance of the obtained results to heterotic strings and to scattering processes involving topology change. It ends with discussion about usefulness of this information for searches of Higgs boson.