Pith. sign in

REVIEW 5 cited by

(3+1)D topological orders with only a $\mathbb{Z}_2$-charged particle

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 2011.11165 v1 pith:7HPZZASD submitted 2020-11-23 math.QA cond-mat.str-elhep-thmath.CT

Theo Johnson-Freyd This is my paper · ORCID
classification math.QAcond-mat.str-elhep-thmath.CT
keywords mathbbparticlegaugeonlypuretheorytopologicaldimensional
verification ladder T0 review T1 audit T2 compute T3 formal

Signed reviews

No signed human review yet.

0 comments
abstract

There is exactly one bosonic (3+1)-dimensional topological order whose only nontrivial particle is an emergent boson: pure $\mathbb{Z}_2$ gauge theory. There are exactly two (3+1)-dimensional topological orders whose only nontrivial particle is an emergent fermion: pure "spin-$\mathbb{Z}_2$" gauge theory, in which the dynamical field is a spin structure; and an anomalous version thereof. I give three proofs of this classification, varying from hands-on to abstract. Along the way, I provide a detailed study of the braided fusion $2$-category $\mathcal{Z}_{(1)}(\Sigma \mathbf{SVec})$ of string and particle operators in pure spin-$\mathbb{Z}_2$ gauge theory.

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 5 Pith papers

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

  1. Non-Clifford quantum cellular automata from invertible topological quantum field theories

    quant-ph 2026-07 conditional novelty 8.0 of 10

    Invertible TQFT data is converted into explicit bounded-range quantum cellular automata, yielding new non-Clifford families and proving that the 5D w3^2 and w2^3 automorphisms are finite-depth circuits.

  2. 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.

  3. Mutual Influence of Symmetries and Topological Field Theories

    math-ph 2025-07 conditional novelty 7.0 of 10

    The supercohomology cocycle of a fermionic fusion 2-category symmetry shifts with period 1, 2, or 4 under stacking with Spin(n)_1 and condensing, depending on the class κ, matching the image of the central charge map.

  4. String-Membrane-Nets from Higher-Form Gauging: An Alternate Route to $p$-String Condensation

    cond-mat.str-el 2025-05 conditional novelty 7.0 of 10

    Gauging a diagonal 1-form symmetry of stacked 2+1D topological orders implements p-string condensation, yielding 3+1D fracton phases such as the X-Cube and string-membrane-net models.

  5. Non-Invertible Symmetries as Condensation Defects in Finite-Group Gauge Theories

    cond-mat.str-el 2024-12 conditional novelty 6.0 of 10

    Non-invertible symmetries in finite-group gauge theories are realized as condensation defects, with a complete Z_N dictionary and new automorphism symmetry expressions.

Pith tools