Gravitational origin of the weak interaction's chirality

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.