Emergent non-commutative matter fields from Group Field Theory models of quantum spacetime

TL;DR

This paper discusses how non-commutative matter fields naturally emerge from Group Field Theory models of quantum spacetime, bridging discrete quantum gravity and effective continuum physics in various dimensions and signatures.

Contribution

It demonstrates a mechanism for deriving non-commutative matter fields directly from GFT actions in 3 and 4 dimensions, advancing the understanding of quantum gravity to matter coupling.

Findings

Non-commutative matter fields emerge from GFT models.

Applicable in both Riemannian and Lorentzian signatures.

Bridges discrete quantum spacetime with continuum physics.

Abstract

We offer a perspective on some recent results obtained in the context of the group field theory approach to quantum gravity, on top of reviewing them briefly. These concern a natural mechanism for the emergence of non-commutative field theories for matter directly from the GFT action, in both 3 and 4 dimensions and in both Riemannian and Lorentzian signatures. As such they represent an important step, we argue, in bridging the gap between a quantum, discrete picture of a pre-geometric spacetime and the effective continuum geometric physics of gravity and matter, using ideas and tools from field theory and condensed matter analog gravity models, applied directly at the GFT level.