Pith Number

pith:ONJOXKWH

pith:2026:ONJOXKWHUAKXODUO4UFCE5ZRIF

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Non-Invertible Symmetries and Boundaries for Two-Dimensional Fermions

Guillermo Arias-Tamargo, Maxwell L. Vel\'asquez Cotini Hutt, Philip Boyle Smith, Rishi Mouland

Two free complex Weyl fermions have anomaly-free Z_k symmetries for each primitive Pythagorean triple, each producing a non-invertible defect that generates all U(1)^2-preserving conformal boundaries.

arxiv:2605.13952 v1 · 2026-05-13 · hep-th · cond-mat.str-el

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Claims

C1strongest claim

We determine all anomaly-free invertible global symmetries of two free complex Weyl fermions, which take the form Z_k for each primitive Pythagorean triple a^2 + b^2 = k^2. ... 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.

C2weakest assumption

The assumption that gauging any of these Z_k symmetries renders the theory self-dual, allowing the non-invertible defects to be well-defined and to generate all listed boundary conditions without additional anomalies or inconsistencies.

C3one line summary

Z_k symmetries from Pythagorean triples in two free Weyl fermions yield non-invertible defects that generate all U(1)^2-preserving boundaries for two Dirac fermions.

References

58 extracted · 58 resolved · 15 Pith anchors

[1] K. Jensen, E. Shaverin and A. Yarom,’t Hooft anomalies and boundaries,Journal of High Energy Physics2018(2018) 2018

[2] R. Thorngren and Y. Wang,Anomalous symmetries end at the boundary,Journal of High Energy Physics2021(2021) 2021

[3] Boundary conformal field theory and symmetry protected topological phases in $2+1$ dimensions 2017 · arXiv:1704.01193

[4] L. Li, C.-T. Hsieh, Y. Yao and M. Oshikawa,Boundary conditions and anomalies of conformal field theories in 1+1 dimensions,Phys. Rev. B110(2024) 045118 [2205.11190] 2024

[5] Boyle Smith and D 2020

Formal links

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Cited by

1 paper in Pith

Non-invertible Symmetries in Weyl Fermions, and Applications to Fermion-Boundary Scattering Problem

Receipt and verification

First computed	2026-05-17T23:39:13.719445Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7352ebaac7a015770e8ee50a22773141465dd543640e31024b565c34e258dedc

Aliases

arxiv: 2605.13952 · arxiv_version: 2605.13952v1 · doi: 10.48550/arxiv.2605.13952 · pith_short_12: ONJOXKWHUAKX · pith_short_16: ONJOXKWHUAKXODUO · pith_short_8: ONJOXKWH

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/ONJOXKWHUAKXODUO4UFCE5ZRIF \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 7352ebaac7a015770e8ee50a22773141465dd543640e31024b565c34e258dedc

Canonical record JSON

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    "abstract_canon_sha256": "1af71e433f0749915045deb901ae54571be81719fcb4506dec86e664b450042b",
    "cross_cats_sorted": [
      "cond-mat.str-el"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "hep-th",
    "submitted_at": "2026-05-13T18:00:00Z",
    "title_canon_sha256": "858b8fac8d46e52b43701f15706b39efce9cc0d16bceae0e317a79eb8618ef46"
  },
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  "source": {
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    "kind": "arxiv",
    "version": 1
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}