Spin foams as Feynman diagrams

TL;DR

This paper demonstrates that any spin foam model can be derived from a field theory framework, which naturally incorporates a sum over triangulations and 2-complexes, leading to a background-independent quantum gravity formulation.

Contribution

It provides an explicit field theory formulation for arbitrary spin foam models, enabling a sum over triangulations and 2-complexes, thus generalizing previous specific cases.

Findings

Any spin foam model can be obtained from a field theory.

The formulation is background independent and sums over triangulations.

Explicit action form for arbitrary spin foam models is provided.

Abstract

It has been recently shown that a certain non-topological spin foam model can be obtained from the Feynman expansion of a field theory over a group. The field theory defines a natural ``sum over triangulations'', which removes the cut off on the number of degrees of freedom and restores full covariance. The resulting formulation is completely background independent: spacetime emerges as a Feynman diagram, as it did in the old two-dimensional matrix models. We show here that any spin foam model can be obtained from a field theory in this manner. We give the explicit form of the field theory action for an arbitrary spin foam model. In this way, any model can be naturally extended to a sum over triangulations. More precisely, it is extended to a sum over 2-complexes.