{"knowledge_schema": {"broad_category": "Theoretical Physics \u2192 Quantum Field Theory \u2192 Anomalies in Gauge Theories", "refinement": "The 't Hooft anomaly matching condition specifically addresses the relationship between ultraviolet (UV) and infrared (IR) behaviors of quantum field theories, particularly in the context of non-Abelian gauge theories.", "specific_scope": "The condition states that the anomalies present in the UV theory must match those in the IR effective theory, ensuring consistency across different energy scales.", "goal": "To ensure that the low-energy effective theory correctly reflects the symmetries and anomalies of the high-energy theory, thereby maintaining physical consistency."}, "summary": "The 't Hooft anomaly matching condition in non-Abelian gauge theories implies that the anomalies of a high-energy (UV) theory must match those of the low-energy (IR) effective theory. This condition ensures consistency between the two regimes and serves as a constraint on the low-energy effective theories, guiding the understanding of symmetry realizations and the behavior of the theory across different energy scales."}