Encoding simplicial quantum geometry in group field theories

TL;DR

This paper introduces a new symmetry requirement in group field theories that enhances the encoding of 3D simplicial quantum geometry, resulting in Feynman amplitudes resembling Regge calculus and clearer geometric relations.

Contribution

It proposes a novel symmetry condition in extended GFT formalism that improves the representation of simplicial geometry in 3D quantum gravity models.

Findings

Feynman amplitudes match simplicial path integrals based on Regge action

Proper relation established between discrete connection and triad vectors

Enhanced geometric encoding at the GFT action level

Abstract

We show that a new symmetry requirement on the GFT field, in the context of an extended GFT formalism, involving both Lie algebra and group elements, leads, in 3d, to Feynman amplitudes with a simplicial path integral form based on the Regge action, to a proper relation between the discrete connection and the triad vectors appearing in it, and to a much more satisfactory and transparent encoding of simplicial geometry already at the level of the GFT action.