Confining strings and anomalies in circle-compactified gauge theories

 

Compactifying large classes of Yang-Mills theories on a  small circle allows for theoretically controlled studies of nonperturbative phenomena such as confinement, the thermal deconfinement transition, and chiral symmetry breaking. After discussing the motivation for these studies, I shall give a brief review (out of necessity often pictorial) of the general setup and main features of the underlying dynamics. In the main part of the talk I have chosen to focus on a single aspect: the confining strings’ properties. I will argue that owing to the unbroken zero-form center symmetry, they come closest (among the models with calculable confinement, notably Seiberg-Witten theory) to those expected of strings in non-supersymmetric pure Yang-Mills theory. Another bonus—and perhaps a tool to push these studies into new regimes—is the intuitive manifestation of the recently discovered mixed zero- and one-form discrete ’t Hooft anomalies in this framework.