Spontaneous Symmetry Breaking in Graviweak Theory

TL;DR

This paper explores a unification of gravity and the weak interaction through spontaneous symmetry breaking in a graviweak theory, predicting novel couplings between gravitons and weak bosons.

Contribution

It introduces a spontaneous symmetry breaking mechanism within a graviweak unification framework, including generalizations in MacDowell-Mansouri theories and predicts new graviton-weak boson interactions.

Findings

Unification of gravity and weak interaction via spontaneous symmetry breaking.

Prediction of non-minimal coupling between curvature and weak gauge fields.

Potential quantum channel between gravitons and weak bosons.

Abstract

Graviweak theory seeks to unify gravity (specifically in its self-dual formulation) with the weak interaction, preying on their parallel chiral $SU(2)$ structures. In this paper we further this idea by folding it with the concept of spontaneous symmetry breaking. We do this first with a standard Higgs field and potential, starting with a unifying parity-invariant theory which splits into the usual gravity and weak sector under spontaneous symmetry breaking. By rewriting the theory in the two-spin framework we are then prompted to discuss generalizations, within the generic approach known as MacDowell-Mansouri theories where a larger internal gauge group is broken. One of the predictions of the ensuing construction is a non-minimal coupling in the low energy broken phase between curvature and the weak gauge fields, translating at the quantum level to a direct channel between the graviton and the weak bosons.