REVIEW 5 cited by
Hecke Relations, Cosets and the Classification of 2d RCFTs
Not yet reviewed by Pith; the record is open.
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
Hecke Relations, Cosets and the Classification of 2d RCFTs
read the original abstract
We systemically study the Hecke relations and the $c=8k$ coset relations among 2d rational conformal field theories (RCFTs) with up to seven characters. We propose that the characters of any 2d RCFT -- unitary or non-unitary -- satisfying a holomorphic modular linear differential equation (MLDE) can be realized as either a Hecke image or the coset of a Hecke image with respect to a $c=8k$ theory. Benefited from the recent results on holomorphic modular bootstrap, we check this proposal for all admissible theories with up to five characters. We also find many new interesting Hecke relations. For example, the characters of WZW models $(E_{6})_2,(E_7)_2,(E_{7\frac12})_2$ can be realized as the Hecke images $\mathsf{T}_{13},\mathsf{T}_{19},\mathsf{T}_{19}$ of Virasoro minimal models $M_{\rm sub}(7,6),M(5,4),M_{\rm eff}(13,2)$ respectively. Besides, we find the characters associated to the second largest Fisher group $Fi_{23}$ and the Harada-Norton group $HN$ can be realized as the Hecke images $\mathsf{T}_{23},\mathsf{T}_{19}$ of the product theories $M_{\rm eff}(5,2)\otimes M_{\rm eff}(7,2)$ and $M_{\rm eff}(7,2)^{\otimes 2}$ respectively. Mathematically, our study provides a great many interesting examples of vector-valued modular functions up to rank seven.
Forward citations
Cited by 5 Pith papers
-
Two approaches to the holomorphic modular bootstrap
A vector-valued modular form construction generates new admissible solutions for rational CFT classification from known RCFTs, reproducing all known two-character solutions with Wronskian indices 6 and 8 while extendi...
-
Unlocking the Wronskian Tower: A Simplification of the Holomorphic Modular Bootstrap
A differential operator Θ = η^{-4}D relates MLDE solutions across Wronskian sectors, reducing higher-ℓ quasi-character classification in ranks 2 and 3 to ℓ=0 data and proving the ℓ=2 sign conjecture.
-
Quasi-Characters for three-character Rational Conformal Field Theories
All (3,0) admissible solutions are expressed via a universal _3F_2 hypergeometric formula; (3,3) solutions are built from them using Bantay-Gannon duality with only 7 of 15 having proper fusion rules, and further (3,6...
-
Signs, growth and admissibility of quasi-characters and the holomorphic modular bootstrap for RCFT
The work proves that quasi-character coefficients have stabilizing alternating signs and estimates their growth near n ~ c/12 via Frobenius recursion on MLDEs, enabling candidate RCFT characters at arbitrary Wronskian index.
-
Updating the holomorphic modular bootstrap
Admissible solutions to MLDEs with ≤6 characters and c_eff ≤24 are enumerated; tenable ones with good fusion rules are identified, with some linked to specific CFTs and MTC classes.
discussion (0)
Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.