Line operators of gauge theories on non-spin manifolds

• Main Authors: J.P. Ang, Konstantinos Roumpedakis, Sahand Seifnashri
• Format: Article
• Language: English
• Published: SpringerOpen 2020-04-01
• Series: Journal of High Energy Physics
• Subjects: Space-Time Symmetries; Topological Field Theories; Wilson; ’t Hooft and Polyakov loops; Anomalies in Field and String Theories
• Online Access: http://link.springer.com/article/10.1007/JHEP04(2020)087

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.