Abstract
Linear confinement with Casimir scaling of the string tension in confining gauge theories is a consequence of a certain property of the Polyakov loop related to random matrices. This mechanism does not depend on the details of the theories (neither the gauge group nor dimensions) and explains approximate Casimir scaling below string-breaking length. In this paper, we study 3d SU(2) pure Yang-Mills theory numerically and find the same random-matrix behavior for rectangular Wilson loops. We conjecture that this is a universal feature of strongly coupled confining gauge theories.
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Acknowledgments
The authors would like to thank Nadav Drukker, Enrico Rinaldi, Hidehiko Shimada, and Hiromasa Watanabe for the discussions. V. G. thanks STFC for the Doctoral Training Programme funding (ST/W507854-2021 Maths DTP). M. H. thanks his STFC consolidated grant ST/X000656/1. G. B. is funded by the Deutsche Forschungsgemeinschaft (DFG) under Grant No. 432299911 and 431842497.
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Bergner, G., Gautam, V., Hanada, M. et al. Wilson loops and random matrices. J. High Energ. Phys. 2024, 203 (2024). https://doi.org/10.1007/JHEP07(2024)203
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DOI: https://doi.org/10.1007/JHEP07(2024)203