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.
Highlights
In quantum gauge theories, string tensions are characteristic properties of confinement phenomena, as they specify the static quark-antiquark potentials
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. 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
The behavior at intermediate distances is curious: the theory is already confining, but the string tensions are not characterized by center symmetry alone
Summary
In quantum gauge theories, string tensions are characteristic properties of confinement phenomena, as they specify the static quark-antiquark potentials. (2) At intermediate distances, the potential becomes linear, with a string tension Tα depending on α. We can nicely describe the relevant selection rule using the center symmetry [9,10], or the 1-form symmetry [11,12] This is not the whole story of confinement. The behavior at intermediate distances is curious: the theory is already confining, but the string tensions are not characterized by center symmetry alone. Driven by this curiosity, the authors were led in Ref. [13] to explore a similar phenomenon in a simpler confining gauge theory in three dimensions, where string tensions at any distance scale do not obey the N-ality rule.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
