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<p>It is known that a two-dimensional bosonic theory with a non-anomalous <i>ℤ</i><sub>2</sub> symmetry can be fermionized. Recent work shows that if the bosonic theory also has non-anomalous time-reversal symmetry, fermionization extends to non-orientable surfaces and yields a fermionic theory that depends on a Pin<sup><i>−</i></sup> structure. Besides fermionization, one can define various topological manipulations, such as gauging and stacking invertible phases, which together generate a web of dualities. We prove that their group structure is the dihedral group <i>D</i><sub>8</sub> of order 16. Furthermore, we systematically investigate the web from two perspectives: Symmetry TFT and actions on sectors of the <i>S</i><sup>1</sup> Hilbert space.</p>

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Web of dualities on non-orientable surfaces

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年5月22日

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  • Ippo Orii,
  • Keita Tsuji

摘要

It is known that a two-dimensional bosonic theory with a non-anomalous ℤ2 symmetry can be fermionized. Recent work shows that if the bosonic theory also has non-anomalous time-reversal symmetry, fermionization extends to non-orientable surfaces and yields a fermionic theory that depends on a Pin− structure. Besides fermionization, one can define various topological manipulations, such as gauging and stacking invertible phases, which together generate a web of dualities. We prove that their group structure is the dihedral group D8 of order 16. Furthermore, we systematically investigate the web from two perspectives: Symmetry TFT and actions on sectors of the S1 Hilbert space.