Group field theory renormalization in the 3D case: Power counting of divergences

Journal Article · Sat Aug 15 00:00:00 EDT 2009 · Physical Review. D, Particles Fields

DOI:https://doi.org/10.1103/PHYSREVD.80.044007· OSTI ID:21322466

Freidel, Laurent; Gurau, Razvan; Oriti, Daniele ^[1]

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1. Perimeter Institute for Theoretical Physics, 31 Caroline St, Waterloo, Ontario N2L 2Y5 (Canada)

We take the first steps in a systematic study of group field theory (GFT) 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 manifoldlike appearance of quantum spacetime at low energies, and of its topology, in a GFT framework.

• OSTI ID: 21322466
• Journal Information: Physical Review. D, Particles Fields, Journal Name: Physical Review. D, Particles Fields Journal Issue: 4 Vol. 80; ISSN PRVDAQ; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
ALGORITHMS
FEYNMAN DIAGRAM
FIELD THEORIES
QUANTUM GRAVITY
RENORMALIZATION
SIMULATION
SPACE-TIME
THREE-DIMENSIONAL CALCULATIONS
TOPOLOGY