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キーワード:
High Energy Physics - Theory, hep-th,General Relativity and Quantum Cosmology, gr-qc,Mathematical Physics, math-ph,Mathematics, Mathematical Physics, math.MP
要旨:
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.
