Diffeomorphisms in group field theories

Abstract

We study the issue of diffeomorphism symmetry in group field theories (GFT), using the recently introduced noncommutative metric representation. 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.

31 pages, revtex4; many figures

References in corpus (8)

• Group field theory with non-commutative metric variables
• Group field theory renormalization - the 3d case: power counting of divergences
• Scaling behaviour of three-dimensional group field theory
• Statistics and UV-IR Mixing with Twisted Poincare Invariance
• Lost in Translation: Topological Singularities in Group Field Theory
• Three Dimensional Quantum Geometry and Deformed Poincare Symmetry
• Braided quantum field theories and their symmetries
• Three dimensional Loop Quantum Gravity: towards a self-gravitating Quantum Field Theory

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• On the finite amplitudes for open graphs in Abelian dynamical colored Boulatov-Ooguri models
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• Comment on `Lost in Translation: Topological Singularities in Group Field Theory'
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• Quantum geometry from higher gauge theory
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• Classical Group Field Theory
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