Web of dualities on non-orientable surfaces

2026/01/14 by Ippo Orii, Keita Tsuji · 1 voice
Physics and Astronomy · #hep-th

paper · pdf · doi:10.1007/jhep05(2026)256

Abstract

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.

Citations

• On dimensions of (2+1)D abelian bosonic topological systems on unoriented manifolds
• Fermionic Non-Invertible Symmetries in (1+1)d: Gapped and Gapless Phases, Transitions, and Symmetry TFTs
• Topological holography for fermions
• ICTP lectures on (non-)invertible generalized symmetries
• Backfiring Bosonisation
• What's Done Cannot Be Undone: TASI Lectures on Non-Invertible Symmetries
• Symmetry TFTs and Anomalies of Non-Invertible Symmetries
• Topological symmetry in quantum field theory
• Bosonic Topological Insulators and Paramagnets: a view from cobordisms
• Symmetry-protected topological orders for interacting fermions -- Fermionic topological nonlinear σ models and a special group supercohomology theory
• Topological phases of fermions in one dimension
• Unpaired Majorana fermions in quantum wires

Discussions

• "Dualities are not accidents. Dualities are just group transformations moving around a finite, structured space of theories". arxiv.org/abs/2601.09067 [bsky, 1 points, 0 comments]

Related

• ℤ_N Duality and Parafermions Revisited
• On finite symmetries and their gauging in two dimensions
• Organizing symmetry-protected topological phases by layering and symmetry reduction: a minimalist perspective
• Z2-topology in nonsymmorphic crystalline insulators: Mobius twist in surface states
• Exploring two dimensional ℤ₂ invariant phases with time reversal symmetry and their transitions with topological operations