Yang-Mills theory vs. T_N quantum mechanics: from double-trace deformations to anomalies.
Abstract: I discuss some old (ten years) and new work on Yang-Mills theory with topological theta angle. A related quantum mechanical system is a particle on a circle with N-minima on the fundamental domain and an Aharonov-Bohm phase (topological theta angle) turned on. In both systems, I will describe 't Hooft anomalies and vacuum structure, and the importance of dihedral groups and its representations. I will present both relatively new ideas, such as double-trace deformations, reliable semi-classics and 't Hooft anomaly matching. In both systems at theta=pi, vacuum is two-fold degenerate (yes, even in 1d QM!) either due to 't Hooft anomaly or global inconsistency.