2018/11/01 by Davide Gaiotto, Theo Johnson-Freyd
Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #Combinatorics #Computer science #Conjecture #Field (mathematics) #Holomorphic function #Mathematics #Pure mathematics #Ternary operation #hep-th #math.KT #math.QA
paper · pdf · doi:10.4153/s0008414x2100002x
23 pages
arxiv created 2018/11/01 · openalex publication_date 2021/01/18 · arxiv updated 2021/01/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Abstract We observe that every self-dual ternary code determines a holomorphic \mathcal N=1 superconformal field theory. This provides ternary constructions of some well-known holomorphic \mathcal N=1 superconformal field theories (SCFTs), including Duncan’s “supermoonshine” model and the fermionic “beauty and the beast” model of Dixon, Ginsparg, and Harvey. Along the way, we clarify some issues related to orbifolds of fermionic holomorphic CFTs. We give a simple coding-theoretic description of the supersymmetric index and conjecture that for every self-dual ternary code this index is divisible by 24 ; we are able to prove this conjecture except in the case when the code has length 12 mod 24 . Lastly, we discuss a conjecture of Stolz and Teichner relating \mathcal N=1 SCFTs with Topological Modular Forms. This conjecture implies constraints on the supersymmetric indexes of arbitrary holomorphic SCFTs, and suggests (but does not require) that there should be, for each k , a holomorphic \mathcal N=1 SCFT of central charge 12k and index 24/gcd (k,24) . We give ternary code constructions of SCFTs realizing this suggestion for k≤ 5 .