Spontaneous Symmetry Breaking in Graviweak Theory

TL;DR

This work develops a graviweak unification framework in which gravity and the weak interaction arise from a common chiral gauge structure within a parity-invariant action. Parity is dynamically broken by a Higgs-like pseudoscalar field with $V(\phi)=(\lambda/4)(\phi^2-1)^2$, yielding $\langle \phi \rangle = \pm 1$ and selecting a left-handed gravitational sector at low energies, yielding an Ashtekar self-dual gravity plus the weak sector. The authors extend the internal Lorentz group to $SO(1,3+N)$ and implement MacDowell–Mansouri–type symmetry breaking, which generically generates nonminimal couplings between curvature and Yang–Mills fields. In the explicit $SO(1,6)$ realization, a direct graviton–weak boson interaction emerges, offering potential observational consequences in gravitational waves and CMB polarization and providing a concrete route to testability with upcoming experiments such as LISA.

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.