Pith. sign in

REVIEW 4 cited by

Construction of two-dimensional topological field theories with non-invertible symmetries

Not yet reviewed by Pith; the record is open.

Re-run · record.json Download PDF Read on arXiv ↗

This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.

SPECIMEN: schema-true, not a live event

T0 review · schema-true

One-sentence machine reading of the paper's core claim.

pith:XXXXXXXX · record.json · timestamp

arxiv 2110.02958 v2 pith:VB46F3R6 submitted 2021-10-06 hep-th cond-mat.str-elmath.CTmath.QA

Tzu-Chen Huang , Ying-Hsuan Lin , Sahand Seifnashri This is my paper · ORCID
classification hep-thcond-mat.str-elmath.CTmath.QA
keywords tftstopologicalcrossingdefectfieldformulaefunctionsnon-invertible
verification ladder T0 review T1 audit T2 compute T3 formal
0 comments
abstract

We construct the defining data of two-dimensional topological field theories (TFTs) enriched by non-invertible symmetries/topological defect lines. Simple formulae for the three-point functions and the lasso two-point functions are derived, and crossing symmetry is proven. The key ingredients are open-to-closed maps and a boundary crossing relation, by which we show that a diagonal basis exists in the defect Hilbert spaces. We then introduce regular TFTs, provide their explicit constructions for the Fibonacci, Ising and Haagerup $\mathcal{H}_3$ fusion categories, and match our formulae with previous bootstrap results. We end by explaining how non-regular TFTs are obtained from regular TFTs via generalized gauging.

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 4 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Non-Local Conserved Currents and Continuous Non-Invertible Symmetries

    hep-th 2025-07 conditional novelty 7.0 of 10

    Non-local conserved currents attached to topological lines generate continuous non-invertible symmetries in 1+1d CFTs, with new examples in SU(2)_k WZW and minimal model products.

  2. Gauging Non-Invertible Symmetries in (2+1)d Topological Orders

    hep-th 2025-07 conditional novelty 7.0 of 10

    A framework for gauging non-invertible symmetries in (2+1)d TQFTs, unifying 0-form and 1-form gauging via surface algebras, with constraints and toric-code examples.

  3. Higher Representations and Quark Confinement

    hep-th 2025-01 conditional novelty 6.0 of 10

    Using higher-categorical representation theory, the paper proposes that the confined and adjoint Higgs phases of scalar QCD are distinguished by their baryon-charge spectra and by the presence of center vortices.

  4. Particle-Soliton Degeneracy in 2D Quantum Chromodynamics

    hep-th 2024-12 conditional novelty 5.0 of 10

    In gapped 2D QCD, a broken non-invertible symmetry forces particles and solitons into degenerate multiplets, encoded as quiver diagrams.

Pith tools