Physics

Spacetime

Symmetry (geometry)

Mathematics

Mathematical physics

String theory

Yang–Mills theory

Casimir effect

Spontaneous symmetry breaking

String (physics)

Global symmetry

Symmetry breaking

Gauge theory

Geometry

Theoretical physics

Quantum mechanics

Classical mechanics

Scaling

Physical review. D/Physical review. D.

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.

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