Spin-cube Models of Quantum Gravity

TL;DR

This paper introduces spin-cube models, a categorical generalization of spin-foam models, for quantum gravity, demonstrating their relation to known models and their correct classical limit.

Contribution

It develops spin-cube models based on a Poincare 2-group, linking them to existing quantum gravity models and analyzing their classical limit.

Findings

Spin-cube models are categorical generalizations of spin-foam models.

They can be reduced to area-Regge or Regge models depending on constraints.

Effective actions have the correct classical limit.

Abstract

We study the state-sum models of quantum gravity based on a representation 2-category of the Poincare 2-group. We call them spin-cube models, since they are categorical generalizations of spin-foam models. A spin-cube state sum can be considered as a path integral for a constrained 2-BF theory, and depending on how the constraints are imposed, a spin-cube state sum can be reduced to a path integral for the area-Regge model with the edge-length constraints, or to a path integral for the Regge model. We also show that the effective actions for these spin-cube models have the correct classical limit.