Non-Invertible Symmetries and Boundaries for Two-Dimensional Fermions

Fuente: arXiv
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Autori principali: Arias-Tamargo, Guillermo, Smith, Philip Boyle, Mouland, Rishi, Hutt, Maxwell L. Velásquez Cotini
Natura: Preprint
Pubblicazione: 2026
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author Arias-Tamargo, Guillermo
Smith, Philip Boyle
Mouland, Rishi
Hutt, Maxwell L. Velásquez Cotini
author_facet Arias-Tamargo, Guillermo
Smith, Philip Boyle
Mouland, Rishi
Hutt, Maxwell L. Velásquez Cotini
contents 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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id arxiv_https___arxiv_org_abs_2605_13952
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle Non-Invertible Symmetries and Boundaries for Two-Dimensional Fermions
Arias-Tamargo, Guillermo
Smith, Philip Boyle
Mouland, Rishi
Hutt, Maxwell L. Velásquez Cotini
High Energy Physics - Theory
Strongly Correlated Electrons
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.
title Non-Invertible Symmetries and Boundaries for Two-Dimensional Fermions
topic High Energy Physics - Theory
Strongly Correlated Electrons
url https://arxiv.org/abs/2605.13952