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

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.

13 pages, no figures; uses JPConf style; contribution to the proceedings of the D.I.C.E. 2008 workshop

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• Effective Hamiltonian Constraint from Group Field Theory
• $\kappa$-Deformations and Extended $\kappa$-Minkowski Spacetimes
• Group field theory and simplicial quantum gravity
• Emergent gravitational dynamics from multi-BEC hydrodynamics?
• Emergent matter from 3d generalised group field theories