Quantum Gravity with Matter via Group Field Theory

Abstract

A generalization of the matrix model idea to quantum gravity in three and higher dimensions is known as group field theory (GFT). In this paper we study generalized GFT models that can be used to describe 3D quantum gravity coupled to point particles. The generalization considered is that of replacing the group leading to pure quantum gravity by the twisted product of the group with its dual --the so-called Drinfeld double of the group. The Drinfeld double is a quantum group in that it is an algebra that is both non-commutative and non-cocommutative, and special care is needed to define group field theory for it. We show how this is done, and study the resulting GFT models. Of special interest is a new topological model that is the ``Ponzano-Regge'' model for the Drinfeld double. However, as we show, this model does not describe point particles. Motivated by the GFT considerations, we consider a more general class of models that are defined using not GFT, but the so-called chain mail techniques. A general model of this class does not produce 3-manifold invariants, but has an interpretation in terms of point particle Feynman diagrams.

43 pages, many figures; v2: one figure, one reference added, minor changes; v3: another model added, discussion expanded; v4: some of the models are removed as uninteresting, paper shortened

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Cited by in corpus (5)

• 3d Spinfoam Quantum Gravity: Matter as a Phase of the Group Field Theory
• Fermions in three-dimensional spinfoam quantum gravity
• Bibliography of Publications related to Classical Self-dual variables and Loop Quantum Gravity
• Exotic Statistics for Strings in 4d BF Theory
• Thermofield Double States in Group Field Theory