Linearized Group Field Theory and Power Counting Theorems

TL;DR

This paper introduces a linearized version of group field theory, providing exact power counting theorems and linking graph homology to amplitude calculations, advancing understanding of quantum gravity models.

Contribution

It presents a novel linearized formulation of group field theory and derives precise power counting theorems, including for colored and nonlinearized models, with connections to graph homology.

Findings

Exact power counting theorems for linearized models

Power counting expressed via graph homology for colored models

Power counting for certain nonlinearized graphs with planarity

Abstract

We introduce a linearized version of group field theory. It can be viewed either as a group field theory over the additive group of a vector space or as an asymptotic expansion of any group field theory around the unit group element. We prove exact power counting theorems for any graph of such models. For linearized colored models the power counting of any amplitude is further computed in term of the homology of the graph. An exact power counting theorem is also established for a particular class of graphs of the nonlinearized models, which satisfy a planarity condition. Examples and connections with previous results are discussed.