Noninvertible 1-form symmetry and Casimir scaling in 2D Yang-Mills theory
Mendel Nguyen, Yuya Tanizaki, Mithat Ünsal
Abstract
Pure Yang-Mills theory in two spacetime dimensions shows exact Casimir scaling. Thus, there are infinitely many string tensions, and this has been understood as a result of nonpropagating gluons in two dimensions. From ordinary symmetry considerations, however, this richness in the spectrum of string tensions seems mysterious. Conventional wisdom has it that it is the center symmetry that classifies string tensions, but being finite it cannot explain infinitely many confining strings. In this paper, we resolve this discrepancy between dynamics and kinematics by pointing out the existence of a noninvertible 1-form symmetry, which is able to distinguish Wilson loops in different representations. We speculate on possible implications for Yang-Mills theories in three and four dimensions.