Pith. sign in

REVIEW 5 cited by

$\mathbb{Z}_N$ Symmetries, Anomalies, and the Modular Bootstrap

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 2101.08343 v2 pith:FKEX3234 submitted 2021-01-20 hep-th cond-mat.str-el

Ying-Hsuan Lin , Shu-Heng Shao This is my paper
classification hep-thcond-mat.str-el
keywords mathbbsymmetrybootstrapconstraintsexistencemodularoperatoranomalies
verification ladder T0 review T1 audit T2 compute T3 formal
0 comments
abstract

We explore constraints on (1+1)$d$ unitary conformal field theory with an internal $\mathbb{Z}_N$ global symmetry, by bounding the lightest symmetry-preserving scalar primary operator using the modular bootstrap. Among the other constraints we have found, we prove the existence of a $\mathbb{Z}_N$-symmetric relevant/marginal operator if $N-1 \le c\le 9-N$ for $N\leq4$, with the endpoints saturated by various WZW models that can be embedded into $(\mathfrak{e}_8)_1$. Its existence implies that robust gapless fixed points are not possible in this range of $c$ if only a $\mathbb{Z}_N$ symmetry is imposed microscopically. We also obtain stronger, more refined bounds that depend on the 't Hooft anomaly of the $\mathbb{Z}_N$ symmetry.

Discussion (0). Sign in to comment.

Forward citations

Cited by 5 Pith papers

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

  1. Non-Invertible Duality Defects in 3+1 Dimensions

    hep-th 2021-11 unverdicted novelty 8.0 of 10

    Constructs non-invertible duality defects for one-form symmetries in 3+1D by partial gauging, derives fusion rules, proves incompatibility with trivial gapped phases, and realizes explicitly in Maxwell theory and latt...

  2. Hypergroup Symmetry in Relative Quantum Field Theories and Chiral Algebras

    hep-th 2026-06 unverdicted novelty 7.0 of 10

    Framework for hypergroup symmetries in relative QFTs establishes one-to-one correspondence between finite symmetries and finite-index conformal embeddings in rational chiral algebras, with implications for gluing left...

  3. Higher Gauging and Non-invertible Condensation Defects

    hep-th 2022-04 unverdicted novelty 7.0 of 10

    Higher gauging of 1-form symmetries on surfaces in 2+1d QFT yields condensation defects whose fusion rules involve 1+1d TQFTs and realizes every 0-form symmetry in TQFTs.

  4. Candidate Gaugings of Categorical Continuous Symmetry

    hep-th 2026-04 unverdicted novelty 6.0 of 10

    Candidate modular invariants and gaugings for continuous G-symmetries with anomaly k are obtained from +1 eigenspaces of semiclassical modular kernels in a BF+kCS SymTFT model.

  5. What's Done Cannot Be Undone: TASI Lectures on Non-Invertible Symmetries

    hep-th 2023-08 unverdicted novelty 3.0 of 10

    A survey of non-invertible symmetries with constructions in the Ising model and applications to neutral pion decay and other systems.

Pith tools