Non-invertible 1-form symmetry and Casimir scaling in 2d Yang-Mills theory

TL;DR

This paper reveals a non-invertible 1-form symmetry in 2D Yang-Mills theory that explains the infinite spectrum of string tensions, resolving a longstanding discrepancy between symmetry principles and dynamical behavior.

Contribution

It introduces a non-invertible 1-form symmetry in 2D Yang-Mills theory, providing a novel symmetry-based explanation for Casimir scaling and the infinite string tension spectrum.

Findings

Identifies a non-invertible 1-form symmetry in 2D Yang-Mills.

Explains the infinite spectrum of string tensions via this symmetry.

Suggests potential implications for higher-dimensional Yang-Mills theories.

Abstract

Pure Yang-Mills theory in 2 spacetime dimensions shows exact Casimir scaling. Thus there are infinitely many string tensions, and this has been understood as a result of non-propagating gluons in 2 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 note, we resolve this discrepancy between dynamics and kinematics by pointing out the existence of a non-invertible 1-form symmetry, which is able to distinguish Wilson loops in different representations. We speculate on possible implications for Yang-Mills theories in 3 and 4 dimensions.