Global inconsistency, 't Hooft anomaly, and level crossing in quantum mechanics

Abstract

An 't Hooft anomaly is the obstruction for gauging symmetries, and it constrains possible low-energy behaviors of quantum field theories by excluding trivial infrared theories. The global inconsistency condition has recently been proposed as a milder condition but is expected to play almost the same role by comparing high symmetry points in the theory space. In order to clarify the consequences of this new condition, we discuss several quantum-mechanical models with topological angles and explicitly compute their energy spectra. It turns out that the global inconsistency can be saturated not only by the ground-state degeneracy at either of the high symmetry points but also by the level crossing (phase transition) separating those high symmetry points.