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Gravity and Yang-Mills Sectors from a Unified Theory and Their Relation with Dark Energy



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PIRSA Number: 
12050079

Abstract

We propose a new method of unifying gravity and the Yang-Mills fields by introducing a spin-foam model. We realize a unification between an SU(2) Yang-Mills interaction and 3D general relativity by considering a constrained Spin(4) ~SO(4) Plebanski action. The theory is quantized a la spin-foam by implementing the analogue of the simplicial constraints for the Spin(4) symmetry, providing a way to couple Yang-Mills fields to spin-foams. 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. We conclude with speculations about extension of the model to 4D and  incorporate a newly developed model of Dark Energy.