Line Operators of Gauge Theories on Non-Spin Manifolds

TL;DR

This paper classifies and analyzes line operators in four-dimensional gauge theories on non-spin manifolds, establishing their spin properties, allowed sets, and related one-form symmetries with anomalies.

Contribution

It introduces a systematic method to assign spins to line operators and classifies all consistent sets for gauge theories with simple Lie algebras.

Findings

Classified all allowed line operators including their spins.

Provided Lagrangian descriptions for these theories.

Computed 't Hooft anomalies for one-form symmetries.

Abstract

We study four-dimensional gauge theories on oriented and non-spin spacetime manifolds. On such manifolds, each line operator arises only either as a boson or a fermion. Based on physical arguments, a method of systematically assigning spin labels to line operators is proposed, and several consistency checks are performed. This is used to classify all possible sets of allowed line operators -- including their spins -- for gauge theories with simple Lie algebras. The Lagrangian descriptions of the theories with these sets of allowed line operators are given. Finally, the one-form symmetries of these theories are studied by coupling to background gauge fields, and their 't Hooft anomalies are computed.