Split gluon masses in $SU(N)\times SU(M)$ theories
Abstract
We extend a known mass-gap equation for pure gluodynamics in global colour models (formulated in equal time quantization in Coulomb gauge) to one in which gluons split into two sets which may have different masses. If the theory is 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 the large scale, such as or similar. We also numerically explore a couple of low-dimensional examples of simple Lie groups, but in spite of the system 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.
Keywords
Cite
@article{arxiv.2309.06114,
title = {Split gluon masses in $SU(N)\times SU(M)$ theories},
author = {Julia Gómez Concejo and Felipe J. Llanes-Estrada and Diego María-Almazán and Alexandre Salas-Bernárdez},
journal= {arXiv preprint arXiv:2309.06114},
year = {2025}
}