Dihedral symmetry in SU(N) Yang-Mills theory

摘要

We point out that charge conjugation and coordinate reflection symmetries do not commute with the center symmetry of SU(N) Yang-Mills (YM) theory when N > 2. As a result, for generic values of the θ angle, the group of discrete 0-form symmetries of YM theory on, e.g., the spacetime manifold R3 × S1 includes the dihedral group D_(2N), which is non-Abelian forN > 2. At θ = π, the non-Abelian factor in the symmetry group is enhanced to D_(4N) due to discrete ’t Hooft anomaly considerations. We illustrate these results in YM theory as well as in a simple quantum mechanical model, where we study representation theory as a function of the θ angle.