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

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arxiv 2104.01824 v2 pith:LDYIP5ON submitted 2021-04-05 hep-th

Mendel Nguyen , Yuya Tanizaki , Mithat Ünsal This is my paper · ORCID
classification hep-th
keywords symmetrydimensionsstringtensionsyang-millscasimirforminfinitely
verification ladder T0 review T1 audit T2 compute T3 formal
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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.

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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Notes on (-2)-form symmetries

    hep-th 2026-06 unverdicted novelty 6.0 of 10

    Introduces (-2)-form symmetries that modify the SymTFT action to relate QFTs differing by anomaly data or non-invertible symmetry associators, illustrated in 2D-4D models, fusion categories, club-sandwich RG flows, an...

  2. SymTFT actions, Condensable algebras and Categorical anomaly resolutions

    hep-th 2025-09 conditional novelty 6.0 of 10

    For Q8 and Rep(Q8), the paper computes condensable algebras, identifies intrinsically gapless SPT phases, and derives fusion-category short exact sequences that resolve categorical anomalies.

  3. Twisted Partition Functions as Order Parameters

    hep-th 2025-05 conditional novelty 5.0 of 10

    Twisted partition functions work as an order parameter that separates broken-symmetry, symmetry-protected, and symmetry-enriched phases, reproduce the Wilson-'t Hooft classification in 4d gauge theories, and tie U(1) ...

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