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<p>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 <i>H</i><sup>3</sup> obstruction, whose nontriviality signals a failure to define symmetry fractionalization consistently. In this short note, we prove that the <i>H</i><sup>3</sup> obstruction for time-reversal symmetry always vanishes in abelian bosonic TQFTs.</p>

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

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  • 发表日期：

    2026年3月2日

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  • Ippo Orii

摘要

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.