Difference between pair creation and anomaly matching: Nontrivial aspects of invertible symmetries and defects in models
This paper investigates the relationship between and Wess-Zumino-Witten models by demonstrating that while anomaly matching imposes a weak condition on their levels, the stricter pairing condition derived from simple currents is necessary to ensure the consistent preservation of symmetries and defects, revealing a fundamental distinction between these two constraints in the context of invertible symmetries.