Spin foam models with finite groups

TL;DR

This paper explores the use of finite groups in spin foam models as a simplified test bed for quantum gravity theories and investigates their potential to exhibit diffeomorphism-like symmetries in lattice frameworks.

Contribution

It introduces finite group-based spin foam models, offering a new approach to quantum gravity research and connecting these models to lattice field theory and condensed matter systems.

Findings

Finite group models serve as effective test beds for quantum gravity.

Potential for finite group models to exhibit analogue diffeomorphism symmetry.

Connections established between quantum gravity models and lattice/condensed matter systems.

Abstract

Spin foam models, loop quantum gravity and group field theory are discussed as quantum gravity candidate theories and usually involve a continuous Lie group. We advocate here to consider quantum gravity inspired models with finite groups, firstly as a test bed for the full theory and secondly as a class of new lattice theories possibly featuring an analogue diffeomorphism symmetry. To make these notes accessible to readers outside the quantum gravity community we provide an introduction to some essential concepts in the loop quantum gravity, spin foam and group field theory approach and point out the many connections to lattice field theory and condensed matter systems.