Semi-Abelian gauge theories, non-invertible symmetries, and string tensions beyond N-ality

• Main Authors: Mendel Nguyen, Yuya Tanizaki, Mithat Ünsal
• Format: Article
• Language: English
• Published: SpringerOpen 2021-03-01
• Series: Journal of High Energy Physics
• Subjects: Confinement; Discrete Symmetries; Global Symmetries; Wilson, ’t Hooft and Polyakov loops
• Online Access: https://doi.org/10.1007/JHEP03(2021)238

Abstract We study a 3d lattice gauge theory with gauge group U(1) N−1 ⋊ S N , which is obtained by gauging the S N global symmetry of a pure U(1) N−1 gauge theory, and we call it the semi-Abelian gauge theory. We compute mass gaps and string tensions for both theories using the monopole-gas description. We find that the effective potential receives equal contributions at leading order from monopoles associated with the entire SU(N) root system. Even though the center symmetry of the semi-Abelian gauge theory is given by ℤ N , we observe that the string tensions do not obey the N-ality rule and carry more detailed information on the representations of the gauge group. We find that this refinement is due to the presence of non-invertible topological lines as a remnant of U(1) N−1 one-form symmetry in the original Abelian lattice theory. Upon adding charged particles corresponding to W-bosons, such non-invertible symmetries are explicitly broken so that the N-ality rule should emerge in the deep infrared regime.