Non-Abelian tensor gauge fields

George Savvidy

Trudy Matematicheskogo Instituta imeni V.A. Steklova, Problems of modern theoretical and mathematical physics: Gauge theories and superstrings, Tome 272 (2011), pp. 212-226

Résumé

A recently proposed extension of Yang–Mills theory contains non-Abelian tensor gauge fields. The Lagrangian has quadratic kinetic terms, as well as cubic and quartic terms describing nonlinear interaction of tensor gauge fields with the dimensionless coupling constant. We analyze the particle content of non-Abelian tensor gauge fields. In four-dimensional space-time the rank-2 gauge field describes propagating modes of helicity 2 and 0. We introduce interaction of the non-Abelian tensor gauge field with fermions and demonstrate that the free equation of motion for the spinor-vector field correctly describes the propagation of massless modes of helicity 3/2. We have found a new metric-independent gauge invariant density which is a four-dimensional analog of the Chern–Simons density. The Lagrangian augmented by this Chern–Simons-like invariant describes the massive Yang–Mills boson, providing a gauge invariant mass gap for a four-dimensional gauge field theory.