Split gauge-boson mass in SU(N) × SU(M) theories

Abstract

We extend a well-known mass-gap equation for pure gluodynamics in global colour models (formulated in equal-time quantization in Coulomb gauge) to one in which gluons are split into two sets, each exhibiting different masses. If the theory is SU(N) x SU(M) with gluons in both groups having identical couplings (as suggested by Grand Unification arguments at large scales) it is immediate to see that different masses are generated for each subgroup. This global symmetry is not broken, but the split masses erase accidental symmetries that might be present due to the two couplings being the same at a large scale, such as SU(N x M) or similar. We also numerically explore a couple of low-dimensional examples of simple Lie groups, but in spite of the system of equations having a form that would seem to allow spontaneous symmetry breaking, it is not triggered for these groups whose algebra has no ideal, and the dispersion relations for the various gluons converge to the same form.