Parity from gauge symmetry

Abstract

We argue that Left-Right parity symmetry $\mathcal{P}$ can arise as a discrete remnant of a unified gauge symmetry. The high-energy unification necessarily includes the gauging of the Lorentz symmetry, bringing into the game gravitational interactions, and leading to a gravi-GUT scheme. Parity emerges unbroken below the Planck scale, and can be broken spontaneously at lower energies making contact with the Standard Model. This framework motivates the spontaneous origin of parity violation as in Left-Right symmetric theories with $\mathcal{P}$. The possible unifying gauge groups are identified as SO(1,7) for gravitational and weak interactions, or SO(7,7) for a complete unification.