Diffeomorphisms in group field theories

Journal Article · Sun May 15 04:00:00 EDT 2011 · Physical Review. D, Particles Fields

DOI:https://doi.org/10.1103/PHYSREVD.83.104051· OSTI ID:21502622

Baratin, Aristide ^[1]; Girelli, Florian ^[2]; Oriti, Daniele ^[3]

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1. Triangle de la Physique, CPHT Ecole Polytechnique, IPhT Saclay, LPT Orsay and Laboratoire de Physique Theorique, CNRS UMR 8627, Universite Paris XI, F-91405 Orsay Cedex (France)
2. School of Physics, University of Sydney, Sydney, New South Wales 2006 (Australia)
3. Max Planck Institute for Gravitational Physics, Albert Einstein Institute, Am Muehlenberg 1, 14467 Golm (Germany)

We study the issue of diffeomorphism symmetry in group field theories (GFT), using the noncommutative metric representation introduced by A. Baratin and D. Oriti [Phys. Rev. Lett. 105, 221302 (2010).]. In the colored Boulatov model for 3d gravity, we identify a field (quantum) symmetry which ties together the vertex translation invariance of discrete gravity, the flatness constraint of canonical quantum gravity, and the topological (coarse-graining) identities for the 6j symbols. We also show how, for the GFT graphs dual to manifolds, the invariance of the Feynman amplitudes encodes the discrete residual action of diffeomorphisms in simplicial gravity path integrals. We extend the results to GFT models for higher-dimensional BF theories and discuss various insights that they provide on the GFT formalism itself.

• OSTI ID: 21502622
• Journal Information: Physical Review. D, Particles Fields, Journal Name: Physical Review. D, Particles Fields Journal Issue: 10 Vol. 83; ISSN PRVDAQ; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
AMPLITUDES
COMMUTATION RELATIONS
FIELD THEORIES
GRAVITATION
INTEGRALS
INVARIANCE PRINCIPLES
MATHEMATICS
METRICS
PATH INTEGRALS
QUANTUM FIELD THEORY
QUANTUM GRAVITY
QUANTUM GROUPS
RACAH COEFFICIENTS
SYMMETRY
SYMMETRY GROUPS
TOPOLOGY