Group field theory renormalization - the 3d case: power counting of divergences

Abstract

We take the first steps in a systematic study of Group Field Theory renormalization, focusing on the Boulatov model for 3D quantum gravity. We define an algorithm for constructing the 2D triangulations that characterize the boundary of the 3D bubbles, where divergences are located, of an arbitrary 3D GFT Feynman diagram. We then identify a special class of graphs for which a complete contraction procedure is possible, and prove, for these, a complete power counting. These results represent important progress towards understanding the origin of the continuum and manifold-like appearance of quantum spacetime at low energies, and of its topology, in a GFT framework.

References in corpus (6)

• A new spinfoam vertex for quantum gravity
• A New Spin Foam Model for 4d Gravity
• The loop-quantum-gravity vertex-amplitude
• Flipped spinfoam vertex and loop gravity
• Vanishing of Beta Function of Non Commutative ${\Phi }_4^4$ Theory to all orders
• The Ponzano-Regge model

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• Towards classical geometrodynamics from Group Field Theory hydrodynamics
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• Dynamics of anisotropies close to a cosmological bounce in quantum gravity
• Properties of Quantum Graphity at Low Temperature
• Gravity as an emergent phenomenon: a GFT perspective
• On the depth of quantum space
• Translation-Invariant Noncommutative Renormalization
• Combinatorics of random tensor models
• Aspects of quantum gravity
• Transition Amplitudes in 3D Quantum Gravity: Boundaries and Holography in the Coloured Boulatov Model