title: Gauge symmetries in spin-foam gravity: the case for "cellular quantization".
abstract: The spin-foam 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 spin-foam 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, and (4) corresponds to its loop quantization. These results significantly clarify the foundations--and limitations--of the spin-foam formalism and open the path to understanding, in a discrete setting, the symmetry-breaking which reduces BF theory to gravity.
authors.affiliation: Perimeter Institute for Theoretical Physics, 31 Caroline Street North, Onatario N2L 2Y5, Waterloo, Canada. vbonzom@perimeterinstitute.ca
authors.forename: Valentin
authors.initials: V
authors.lastname: Bonzom
authors.forename: Matteo
authors.initials: M
authors.lastname: Smerlak