Symmetric Gapped States and Symmetry-Enforced Gaplessness in 3-dimension
This paper establishes a comprehensive framework in three spatial dimensions that classifies fermionic quantum anomalies into two distinct classes—those permitting symmetric gapped phases and those enforcing gaplessness—thereby providing concrete predictions for the infrared behavior of (3+1)-dimensional gauge theories and demonstrating that discrete chiral anomalies cannot be trivialized by adding bosonic degrees of freedom.