Emergent matter from 3d generalised group field theories
Alessandro Di Mare, Daniele Oriti
TL;DR
The paper investigates whether matter can emerge as a phase of a generalized 3d group field theory by solving the classical equations of motion and studying perturbations around those solutions. It finds that perturbations in the group sector can realize a noncommutative scalar field theory on momentum space, signaling emergent matter, while perturbations in the Lie algebra sector fail to produce the expected noncommutative structure, revealing limitations of the generalized GFT formalism. The authors derive exact and approximate solutions for both the static-ultralocal truncation and the full model, highlighting where the approach succeeds and where it falls short, and they argue that a noncommutative reformulation (e.g., via a noncommutative Fourier transform) may be required to realize the intended BF-like dynamics from the outset. These findings inform the viability of matter emergence from quantum geometry and guide improvements in GFT frameworks for quantum gravity phenomenology.
Abstract
We identify classical solutions of a generalised group field theory model in 3 dimensions, and study the corresponding perturbations, deriving their effective dynamics. We discuss their interpretation as emergent matter fields. This allows us, on the one hand to test the proposed mechanism for emergence of matter as a phase of group field theory, and on the other hand to expose some limitations of the generalised group field theory formalism.