A BRST view of the spontaneous symmetry breaking

TL;DR

This paper explores how BRST symmetry can be used to understand the splitting of gauge couplings during spontaneous symmetry breaking in GUTs, providing a cohomological framework for the transition.

Contribution

It introduces a novel BRST-based approach to analyze the coupling splitting in GUT symmetry breaking, linking cohomology to physical phase transitions.

Findings

BRST operator in symmetric phase predicts a single coupling

Proposes a modified BRST operator for the asymmetric phase

Provides a cohomological interpretation of coupling splitting

Abstract

After the phase transition of a Grand Unified Theory (GUT), its single coupling splits into the couplings of the basic interactions. On the other side, the measurement of the Weinberg mixing angle in the eletroweak theory determines that the couplings associated to the SU(2) and U(1) symmetries were already distinct in its symmetric phase, before the electroweak breaking. This picture is consistent as we understand that such couplings evolve independently with the energy scale, meeting a common point together with the strong interaction coupling at the GUT scale. From a BRST symmetry point of view, this implies that each independent coupling should be associated to independent cocycles defined on a cohomological basis. The problem is that, before the GUT symmetry breaking, the BRST operator associated to this symmetric phase predicts a single Yang-Mills coupling. This sets the question of what should be the BRST operator of the asymmetric phase, that would allow for the splitting of this coupling but at the same time remain compatible with the BRST operator of the symmetric phase. In this work we proceed to answer this question.