Pith. sign in

REVIEW 6 cited by

Galois Symmetry Induced by Hecke Relations in Rational Conformal Field Theory and Associated Modular Tensor Categories

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 1912.11955 v3 pith:GAW7AGRS submitted 2019-12-27 hep-th cond-mat.str-elmath.NTmath.RT

Jeffrey A. Harvey , Yichen Hu , Yuxiao Wu This is my paper · ORCID
classification hep-thcond-mat.str-elmath.NTmath.RT
keywords galoisheckemodularfieldoperatorssymmetrytheoriescategories
verification ladder T0 review T1 audit T2 compute T3 formal

Signed reviews

No signed human review yet.

0 comments
abstract

Hecke operators relate characters of rational conformal field theories (RCFTs) with different central charges, and extend the previously studied Galois symmetry of modular representations and fusion algebras. We show that the conductor $N$ of a RCFT and the quadratic residues mod $N$ play an important role in the computation and classification of Galois permutations. We establish a field correspondence in different theories through the picture of effective central charge, which combines Galois inner automorphisms and the structure of simple currents. We then make a first attempt to extend Hecke operators to the full data of modular tensor categories. The Galois symmetry encountered in the modular data appears in the fusion and the braiding matrices as well, and yields isomorphic structures in theories related by Hecke operators.

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 6 Pith papers

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

  1. 3d $\mathcal N=4$ rank-zero mirror symmetry, TQFT interfaces, and Zagier duality of Nahm sums

    hep-th 2026-08 conditional novelty 8.0 of 10

    Zagier duality between the (E8,T1) and (T1,E8) Nahm systems is realized as 3d N=4 rank-zero mirror symmetry of two U(1)^8 Chern-Simons matter theories, with the duality interface generating the level-one E8 character.

  2. 3d $\mathcal{N}=$ 4 rank-0 SCFT from punctured lens space

    hep-th 2026-08 conditional novelty 7.0 of 10

    The Gang-Kim-Stubbs rank-0 SCFT is derived from the Dimofte-Gaiotto-Gukov construction on a punctured lens space, and a new family of theories plus a self-mirror conjecture are proposed from other lens spaces.

  3. Parafermionizing the Monster

    hep-th 2026-05 unverdicted novelty 7.0 of 10

    Parafermionization equates the Monster CFT to a gauged parafermion pair, yielding Rep(so(3)_p) symmetry and defect McKay-Thompson series invariant under Gamma_1(p+2).

  4. Character Identities Between Affine and Virasoro Vertex Operator Algebra Modules

    math.QA 2025-11 conditional novelty 6.0 of 10

    Admissible-level affine sl2 modules and rational Virasoro minimal-model modules have matching characters under the substitution (w,q) -> (q^{+/-1/2}, q^3).

  5. Organizing transitions and their cascades: Generalized symmetry enforcement in massless flows or Higgs transitions

    hep-th 2026-08 conditional novelty 5.0 of 10

    The unbroken fusion ring symmetry FR(SU(2)_{p-2}) stabilizes the massless RG flow M(p,p+1)->M(p-1,p) by making every invariant IR primary field irrelevant.

  6. Gauging or extending bulk and boundary conformal field theories: Application to bulk and domain wall problem in topological matter and their descriptions by (mock) modular covariant

    hep-th 2024-12 conditional novelty 5.0 of 10

    New classes of boundary and coupled conformal field theories are constructed from Z_N gauging, with a proposed dictionary to topological order, nonchiral anyons, and domain walls.

Pith tools