Character Vectors of Strongly Regular Vertex Operator Algebras

Symmetry Integrability and Geometry-Methods and Applications

article

Cameron Franc¹  Geoffrey Mason² 

[1] McMaster University;UCSC

关键词: vertex operator algebras;    conformal field theory;    modular forms.;   

DOI  :  10.3842/SIGMA.2022.085

来源: National Academy of Science of Ukraine

【 摘 要 】

We summarize interactions between vertex operator algebras and number theory through the lens of Zhu theory. The paper begins by recalling basic facts on vertex operator algebras (VOAs) and modular forms, and then explains Zhu's theorem on characters of VOAs in a slightly new form. We then axiomatize the desirable properties of modular forms that have played a role in Zhu's theorem and related classification results of VOAs. After this we summarize known classification results in rank two, emphasizing the geometric theory of vector-valued modular forms as a means for simplifying the discussion. We conclude by summarizing some known examples, and by providing some new examples, in higher ranks. In particular, the paper contains a number of potential character vectors that could plausibly correspond to a VOA, but such that the existence of a corresponding hypothetical VOA is presently unknown.

【 授权许可】

Unknown