Gribov problem in the eletroweak and gluon confined theories

Abstract

We show that gauge fields after a spontaneous symmetry breaking (SSB) mechanism do not have a Gribov problem along the broken directions. In order to make this proof, we describe a gauge fixing procedure inspired on Morse’s theory leading to the concept of a gauge fixing generating functional. This approach is specially suited in order to understand the unitary gauges of ’t Hooft. The conclusion is that after a SSB process, the generalized Faddeev-Popov operator acquires a positive definite value along the broken directions. We show how this works in the eletroweak SU(2)XU(1) theory, where such a result is in fact expected as in this case the gauge fields acquire masses after the SSB. Then we apply this development to the SL(3,c) confining model of Amaral [A path to confine gluons and fermions through complex gauge theory, ]. The final result explains why such confining mechanism is actually a solution to the Gribov problem for the confined gauge fields. These cases show that although confinement is not a general effect of the solution of the Gribov problem, as we can infer from the eletroweak example, its solution indeed seems to be necessary in order to achieve confinement. In the end, these conclusions allow us to speculate that the strong interaction confinement may be the result of some hidden SSB mechanism yet to be described. Published by the American Physical Society 2024