Bubbles and jackets: new scaling bounds in topological group field theories
arXiv:1203.5082 · doi:10.1007/JHEP06(2012)092
Abstract
We use a reformulation of topological group field theories in 3 and 4 dimensions in terms of variables associated to vertices, in 3d, and edges, in 4d, to obtain new scaling bounds for their Feynman amplitudes. In both 3 and 4 dimensions, we obtain a bubble bound proving the suppression of singular topologies with respect to the first terms in the perturbative expansion (in the cut-off). We also prove a new, stronger jacket bound than the one currently available in the literature. We expect these results to be relevant for other tensorial field theories of this type, as well as for group field theory models for 4d quantum gravity.
v2: Minor modifications to match published version
References in corpus (12)
- LQG vertex with finite Immirzi parameter
- A New Spin Foam Model for 4d Gravity
- Flipped spinfoam vertex and loop gravity
- Group field theory with non-commutative metric variables
- The 1/N expansion of colored tensor models
- Scaling behaviour of three-dimensional group field theory
- Quantum Gravity on the Lattice
- EPRL/FK Group Field Theory
- Lost in Translation: Topological Singularities in Group Field Theory
- Three Dimensional Quantum Geometry and Deformed Poincare Symmetry
- Holography and the scale-invariance of density fluctuations
- Emergent diffeomorphism invariance in a discrete loop quantum gravity model