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arXiv · 2601.09067

Web of dualities on non-orientable surfaces

Ippo Orii·Keita Tsuji
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Abstract

It is known that a two-dimensional bosonic theory with a non-anomalous $\mathbb{Z}_2$ 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 $\mathrm{Pin}^-$ 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 $D_8$ of order 16. Furthermore, we systematically investigate the web from two perspectives: Symmetry TFT and actions on sectors of the $S^1$ Hilbert space.

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Ippo Orii, Keita Tsuji. 2026-01-14. Web of dualities on non-orientable surfaces. https://doi.org/10.1007/jhep05(2026)256

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