Skip to content
DraconiticResearch
Search Sources API
190,851 studies31 sourcesUpdated 35 min ago
PreprintarXiv licencearXiv

Classification of c=1 CFTs

  • Lorenz Eberhardt
  • Nat Levine
Open at sourcePDFDOICite

Abstract

We completely classify unitary 2d CFTs with central charge c=1 and discrete spectrum. We confirm the folklore that the only such theories are the compact free boson, its ℤ2-orbifold, and three exceptional theories obtained as orbifolds of the SU(2)1 WZW model. The proof is by recasting the c=1 modular bootstrap as a crystalline measure problem for the density of states, and analytically solving it. We also show that, once the density of states is specified, the full CFT can be uniquely reconstructed.

Related

  1. Maximizing the spectral gap for free bosonic CFTs
    Hyeongjoe Chu, Yuchan Jung
    arXivPreprintarXiv licenceFull textGeometry & topologyHigh-energy & particle physicsarXiv
  2. On Integrable Deformations of CFTs and Integrable Two-Dimensional Sigma Models
    Mikhail Alfimov
    arXivPreprintCC BY 4.0Full textMathematical physicsHigh-energy & particle physicsarXiv
  3. Charged AdS3 black branes as marginally deformed two-dimensional CFTs
    Suting Zhao, Gabriel Arenas-Henriquez, Yizhou Lu +2
    arXivPreprintCC BY 4.0Full textMathematical physicsGravitation & general relativityarXiv
  4. Monstrous parafermionic defects and other non-invertible symmetries in chiral CFTs
    Roberto Volpato
    arXivPreprintCC BY 4.0Full textAlgebra & number theoryHigh-energy & particle physicsarXiv
  5. A Classification of Fourier Summation Formulas and Crystalline Measures
    Felipe Gonçalves
    Constructive ApproximationPeer-reviewedLicence not statedFull text7 citedGeneral mathematicsOpenAlex

Cite

BibTeXRIS
BibTeX
@misc{eberhardt2026classification,
  title = {{Classification of c=1 CFTs}},
  author = {Lorenz Eberhardt and Nat Levine},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.16111},
  eprint = {2609.16111},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.16111},
}
RIS
TY  - UNPB
TI  - Classification of c=1 CFTs
AU  - Lorenz Eberhardt
AU  - Nat Levine
PY  - 2026
DA  - 2026/09/14
PB  - arXiv
DO  - 10.48550/arxiv.2609.16111
UR  - https://arxiv.org/abs/2609.16111
AB  - We completely classify unitary 2d CFTs with central charge c=1 and discrete spectrum. We confirm the folklore that the only such theories are the compact free boson, its ℤ_2-orbifold, and three exceptional theories obtained as orbifolds of the SU(2)_1 WZW model. The proof is by recasting the c=1 modular bootstrap as a crystalline measure problem for the density of states, and analytically solving it. We also show that, once the density of states is specified, the full CFT can be uniquely reconstructed.
ER  -