Gravitational origin of the weak interaction's chirality

TL;DR

This paper proposes a unification of weak and gravitational interactions by embedding the weak SU(2) gauge fields into the space-time connection, explaining the weak interaction's chirality through a complexified Lorentz group framework.

Contribution

It introduces a novel unification model combining weak and gravitational interactions via a complexified Lorentz group, revealing the origin of weak chirality and connecting fermions to Higgs-like scalars.

Findings

Weak interactions emerge as the chiral part of the space-time connection.

The theory predicts a stable phase with a graviton and SU(2) gauge fields.

Fermions can be interpreted as chiral neutrinos with Higgs-like scalars.

Abstract

We present a new unification of the electro-weak and gravitational interactions based on the joining the weak SU(2) gauge fields with the left handed part of the space-time connection, into a single gauge field valued in the complexification of the local Lorentz group. Hence, the weak interactions emerge as the right handed chiral half of the space-time connection, which explains the chirality of the weak interaction. This is possible, because, as shown by Plebanski, Ashtekar, and others, the other chiral half of the space-time connection is enough to code the dynamics of the gravitational degrees of freedom. This unification is achieved within an extension of the Plebanski action previously proposed by one of us. The theory has two phases. A parity symmetric phase yields, as shown by Speziale, a bi-metric theory with eight degrees of freedom: the massless graviton, a massive spin two field and a scalar ghost. Because of the latter this phase is unstable. Parity is broken in a stable phase where the eight degrees of freedom arrange themselves as the massless graviton coupled to an SU(2) triplet of chirally coupled Yang-Mills fields. It is also shown that under this breaking a Dirac fermion expresses itself as a chiral neutrino paired with a scalar field with the quantum numbers of the Higgs.