Towards a Loop Quantum Gravity and Yang-Mills Unification

TL;DR

This paper introduces a novel spin-foam model aiming to unify gravity with the Standard Model by combining SU(2) Yang-Mills interactions and 3D general relativity within a Spin(4) framework, with potential for physical predictions.

Contribution

It presents a new spin-foam approach for unifying gravity and gauge interactions, extending to 4D, and proposes a method to compute scattering amplitudes in Loop Quantum Gravity.

Findings

Unified SU(2) Yang-Mills and 3D gravity in a Spin(4) model

Quantization via spin-foam with simplicial constraints

Initial approach to scattering amplitudes in Loop Quantum Gravity

Abstract

We propose a new method of unifying gravity and the Standard Model by introducing a spin-foam model. We realize a unification between an SU(2) Yang-Mills interaction and 3D general relativity by considering a Spin(4) Plebanski action. The theory is quantized a la spin-foam by implementing the analogue of the simplicial constraints for the broken phase of the Spin(4) SO(4) symmetry. A natural 4D extension of the theory is shown. We also present a way to recover 2-point correlation functions between the connections as a first way to implement scattering amplitudes between particle states, aiming to connect Loop Quantum Gravity to new physical predictions.