Gauge Boson Condensation and Symmetry Breaking Patterns in Non-Abelian Gauge Theories

We investigate the possibility that the perturbative vacuum is unstable against gauge boson pair condensation in non-Abelian gauge theories without fundamental scalar fields. The force law between gauge boson pairs is studied in the Coulomb gauge. Assuming that the pairs condense in channels of attractive gauge force, we investigate the patterns of spontaneous symmetry breakdown in the 5U(N) and 50(2N) gauge theories. As a possible application of this symmetry breaking scheme, we consider 5U(5) and 50(10) gauge models of grand unification without fundamental scalar fields. It is found that the desirable breaking patterns 5U(5)~ 5U(3)x 5U(2) x U(1) and 5()(10)~ 50(6) x 0(4)~ 5U(3)X 5U(2) x 5U(2) x U(1) arise as a result of gauge boson pair condensation. Our mechanism is also applicable to GUTs with massless fundamental scalars, in which supercooling of the Universe would last up to extremely low temperature.