2010/01/31 by Arkady L. Kholodenko, ARKADY L. KHOLODENKO
Mathematics · Physics and Astronomy · #Axial symmetry #Black Holes and Theoretical Physics #Correctness #Field (mathematics) #Gauge (firearms) #Gauge theory #Mass gap #Quantum #Quantum Chromodynamics and Particle Interactions #Quantum and Classical Electrodynamics #Symmetry (geometry) #Symmetry group #hep-th #math-ph #math.MP
paper · pdf · doi:10.1142/s0219887811005646
published as International J.of Geom.Methods in Modern Physics 8 (2011) 1355-1418 · 66 pages, version 2, fully revised and updated
arxiv created 2010/08/03 · openalex publication_date 2011/05/03 · arxiv updated 2015/05/14 · openalex created_date 2019/06/27 · openalex updated_date 2026/08/05
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, J. Geom. Phys.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) × SU (2) × U (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.