On two-dimensional quasitopological field theories

TL;DR

This paper explores a class of 2D lattice field theories, including gauge theories, that utilize semi-simple Hopf algebra symmetries, developing character expansions to compute partition functions and Wilson loop expectations.

Contribution

It introduces a broader local symmetry framework using semi-simple Hopf algebras and develops character expansion techniques for quasitopological field theories.

Findings

Partition functions computed via character expansion

Generalized Wilson loops analyzed within the framework

Broader local symmetry implementation demonstrated

Abstract

We study a class of lattice field theories in two dimensions that includes gauge theories. We show that in these theories it is possible to implement a broader notion of local symmetry, based on semi-simple Hopf algebras. A character expansion is developed for the quasitopological field theories, and partition functions are calculated with this tool. Expected values of generalized Wilson loops are defined and studied with the character expansion.