Vanishing of the H³ obstruction for time-reversal symmetry in (2+1)D abelian bosonic TQFTs

2025/09/09 by Ippo Orii, Orii, Ippo
Physics and Astronomy · #Topological Materials and Phenomena #Quantum many-body systems #Black Holes and Theoretical Physics

paper · pdf · doi:10.48550/arxiv.2509.07368

Abstract

In (2+1)-dimensional topological quantum field theories (TQFTs), the action of a global symmetry group on the anyon system is one of the central topics of research. Owing to the subtle categorical nature of anyons, a global symmetry acting on them is generally realized in a projective manner. Symmetry fractionalization encodes this projective realization. The obstruction to defining symmetry fractionalization is captured by a cohomology class, known as the H³ obstruction, whose nontriviality signals a failure to define symmetry fractionalization consistently. In this short note, we prove that the H³ obstruction for time-reversal symmetry always vanishes in abelian bosonic TQFTs.

Citations

• On dimensions of (2+1)D abelian bosonic topological systems on unoriented manifolds
• Reflection fusion categories
• Classification of abelian spin Chern-Simons theories
• Classical and quantum conformal field theory

Cited by

• Generalization of anomaly formula for time reversal symmetry in (2+1)D abelian bosonic TQFTs

Related

• Generalization of anomaly formula for time reversal symmetry in (2+1)D abelian bosonic TQFTs
• When Does A Three-Dimensional Chern-Simons-Witten Theory Have A Time Reversal Symmetry?
• Time-Reversal Symmetry, Anomalies, and Dualities in (2+1)d
• Invertibility of Condensation Defects and Symmetries of 2 + 1d QFTs
• Time-reversal invariant TQFTs from self-mirror symmetric SCFTs