4d Deformed Special Relativity from Group Field Theories

TL;DR

This paper derives a scalar field theory resembling deformed special relativity from a group field theory framework, revealing how matter and non-commutative spacetime structures emerge non-perturbatively in quantum gravity models.

Contribution

It presents a non-perturbative derivation of deformed special relativity from group field theories, connecting quantum gravity, non-commutative geometry, and matter emergence.

Findings

Matter fields emerge as perturbations in the GFT model.

The effective dynamics are governed by a non-commutative field theory.

The model is based on the SO(4,1) group field theory for 4D BF-theory.

Abstract

We derive a scalar field theory of the deformed special relativity type, living on non-commutative kappa-Minkowski spacetime and with a kappa-deformed Poincare symmetry, from the SO(4,1) group field theory defining the transition amplitudes for topological BF-theory in 4 space-time dimensions. This is done at a non-perturbative level of the spin foam formalism working directly with the group field theory (GFT). We show that matter fields emerge from the fundamental model as perturbations around a specific phase of the GFT, corresponding to a solution of the fundamental equations of motion, and that the non-commutative field theory governs their effective dynamics.