Spin state sum models in two dimensions

TL;DR

This paper introduces a novel two-dimensional spin state sum model that incorporates topology and spin structures, revealing dependence on surface spin structures and exploring extensions with defects for richer model classes.

Contribution

It presents a new type of spin state sum model for 2D surfaces, highlighting dependence on spin structures and introducing defects to expand the model's capabilities.

Findings

Models depend on surface spin structure via parity

Explicit examples demonstrate spin structure dependence

Defects can enlarge the class of spin models

Abstract

We propose a new type of state sum model for two-dimensional surfaces that takes into account topology and spin. The definition used - new to the literature - provides a rich class of extended models called spin models. Both examples and general properties are studied. Most prominently, we find this type of model can depend on a surface spin structure through parity alone and we explore explicit cases that feature this behaviour. Further directions for the two dimensional world are analysed: we introduce a source of new information - defects - and show how they can enlarge the class of spin models available.