Bubbles and jackets: new scaling bounds in topological group field theories

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.

arXiv commentv2: Minor modifications to match published version

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• Renormalization of an SU(2) Tensorial Group Field Theory in Three Dimensions
• Functional Renormalisation Group Approach for Tensorial Group Field Theory: a Rank-3 Model
• The 1/N Expansion of Tensor Models Beyond Perturbation Theory
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• Invitation to Random Tensors
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• Bulk amplitude and degree of divergence in 4d spin foams
• Spin foams