Gauge symmetries in spinfoam gravity: the case for "cellular quantization"

Abstract

The spinfoam approach to quantum gravity rests on a "quantization" of BF theory using 2-complexes and group representations. We explain why, in dimension three and higher, this "spinfoam quantization" must be amended to be made consistent with the gauge symmetries of discrete BF theory. We discuss a suitable generalization, called "cellular quantization", which (1) is finite, (2) produces a topological invariant, (3) matches with the properties of the continuum BF theory, (4) corresponds to its loop quantization. These results significantly clarify the foundations - and limitations - of the spinfoam formalism, and open the path to understanding, in a discrete setting, the symmetry-breaking which reduces BF theory to gravity.

6 pages

References in corpus (6)

• The loop-quantum-gravity vertex-amplitude
• Group field theory with non-commutative metric variables
• The Ponzano-Regge model
• Diffeomorphisms in group field theories
• Bubble divergences: sorting out topology from cell structure
• Bubble divergences from twisted cohomology

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• Towards the Turaev-Viro amplitudes from a Hamiltonian constraint
• Quasi-local holographic dualities in non-perturbative 3d quantum gravity
• Bubble divergences and gauge symmetries in spin foams
• 3D holography: from discretum to continuum
• A new Hamiltonian for the Topological BF phase with spinor networks
• Duality between Spin networks and the 2D Ising model
• Origin of the quantum group symmetry in 3d quantum gravity
• Renormalization of group field theories for quantum gravity: new scaling results and some suggestions
• The Construction of Spin Foam Vertex Amplitudes
• 3d Quantum Gravity: Coarse-Graining and q-Deformation
• Lessons from Toy-Models for the Dynamics of Loop Quantum Gravity
• Quantum edge modes in 3d gravity and 2+1d topological phases of matter
• Degenerate Plebanski Sector and Spin Foam Quantization
• Quasi-Local 3D Quantum Gravity : Exact Amplitude and Holography
• Hessian in the spinfoam models with cosmological constant