A Deformed Poincare Invariance for Group Field Theories

TL;DR

This paper demonstrates that Boulatov's group field theory exhibits a global deformed Poincare symmetry, linking quantum gravity models with non-commutative geometry and suggesting new ways to understand geometric states and braiding in these theories.

Contribution

It reveals a previously unnoticed deformed Poincare invariance in Boulatov's theory, connecting group field theories with non-commutative symmetries and geometric state definitions.

Findings

Boulatov's theory is invariant under a deformed Poincare symmetry.

This invariance allows defining flat and excited geometric states.

The analysis highlights the importance of braiding in group field theories.

Abstract

In the context of quantum gravity, group field theories are field theories that generate spinfoam amplitudes as Feynman diagrams. They can be understood as generalizations of the matrix models used for 2d quantum gravity. In particular Boulatov's theory reproduces the amplitudes of the Ponzano-Regge spinfoam model for 3d quantum gravity. Motivated by recent works on field theories on non-commutative flat spaces, we show that Boulatov's theory (and its colored version) is actually invariant under a global deformed Poincare symmetry. This allows to define a notion of flat/excited geometry states when considering scalar perturbations around classical solutions of the group field equations of motion. As a side-result, our analysis seems to point out that the notion of braiding of group field theories should be a key feature to study further in this context.