Noninvertible 1-form symmetry and Casimir scaling in 2D Yang-Mills theory

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.

Automated summary

In 2D Yang-Mills theory, exact Casimir scaling leads to infinitely many string tensions due to nonpropagating gluons. The richness in the spectrum of string tensions, seemingly mysterious from ordinary symmetry considerations, cannot be explained by finite center symmetry. By introducing a noninvertible 1-form symmetry, a discrepancy between dynamics and kinematics is resolved, with potential implications for Yang-Mills theories in 3D and 4D.