Bubble divergences: sorting out topology from cell structure

TL;DR

This paper analyzes bubble divergences in flat spinfoam models, linking topological and cellular structures to divergence degrees, and clarifies their relation to tensor model powercounting and 1/N expansion.

Contribution

It specializes a cohomological divergence evaluation to cell decompositions of pseudomanifolds, connecting topological structures with divergence analysis in spinfoam models.

Findings

Divergence degree can be exactly evaluated using twisted cohomology.

The approach reproduces previous powercounting results for tensor models.

Provides insights into algebraic-topological aspects of Gurau's 1/N expansion.

Abstract

We conclude our analysis of bubble divergences in the flat spinfoam model. In [arXiv:1008.1476] we showed that the divergence degree of an arbitrary two-complex Gamma can be evaluated exactly by means of twisted cohomology. Here, we specialize this result to the case where Gamma is the two-skeleton of the cell decomposition of a pseudomanifold, and sharpen it with a careful analysis of the cellular and topological structures involved. Moreover, we explain in detail how this approach reproduces all the previous powercounting results for the Boulatov-Ooguri (colored) tensor models, and sheds light on algebraic-topological aspects of Gurau's 1/N expansion.