Abstract

String tension is one of the characteristic quantity in confining gauge theories. In SU(N) gauge theories, there is a center symmetry, or Z_N 1-form symmetry, which acts on the test quarks, and this is the symmetry which controls the spectral properties of confining strings in the infrared regime. This is sometimes called as an N-ality rule. In this talk, I will construct a simple toy model, which we call the 3d semi-Abelian gauge theory, and the N-ality rule is violated there. That is, the center symmetry is again given by Z_N as in the case of SU(N) theory, while the confining strings of Wilson loops carry detailed information on their representations beyond N-ality. Then, I will uncover that our model enjoys the non-invertible symmetry, and they can naturally explain why the N-ality rule can be violated. I would also like to talk about speculation on possible applicability to non-Abelian gauge theories. This talk is based on the work, https://arxiv.org/abs/2101.02227, in collaboration with Mendel Nguyen and Mithat Unsal.