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arXiv · 2605.13952

Non-Invertible Symmetries and Boundaries for Two-Dimensional Fermions

Guillermo Arias-Tamargo·Philip Boyle Smith·Rishi Mouland·Maxwell L. Velásquez Cotini Hutt
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Abstract

We study the relation between boundary conditions and categorical symmetries of two-dimensional fermionic conformal field theories. We determine all anomaly-free invertible global symmetries of two free complex Weyl fermions, which take the form $\mathbb{Z}_k$ for each primitive Pythagorean triple $a^2 + b^2 = k^2$. The theory is self-dual under gauging any of these symmetries, and so to each there is associated a non-invertible topological defect. We study the properties of these lines, and show that any conformal boundary condition of two Dirac fermions that preserves a $U(1)^2$ symmetry can be found by dressing a trivial Dirichlet boundary with one of them. We discuss two microscopic descriptions of these defects: fermions coupled to a quantum-mechanical rotor degree of freedom; and an abelian gauge theory that realises symmetric mass generation in a half-space.

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Guillermo Arias-Tamargo, Philip Boyle Smith, Rishi Mouland, Maxwell L. Velásquez Cotini Hutt. 2026-05-13. Non-Invertible Symmetries and Boundaries for Two-Dimensional Fermions. https://arxiv.org/abs/2605.13952

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