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ЖУРНАЛЫ // Symmetry, Integrability and Geometry: Methods and Applications // Архив

SIGMA, 2022, том 18, 085, 49 стр. (Mi sigma1881)

Эта публикация цитируется в 1 статье

Character Vectors of Strongly Regular Vertex Operator Algebras

Cameron Franca, Geoffrey Masonb

a McMaster University, Canada
b UCSC, USA

Аннотация: 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.

Ключевые слова: vertex operator algebras, conformal field theory, modular forms.

MSC: 17B69, 18M20, 11F03

Поступила: 11 декабря 2021 г.; в окончательном варианте 13 октября 2022 г.; опубликована 29 октября 2022 г.

Язык публикации: английский

DOI: 10.3842/SIGMA.2022.085



Реферативные базы данных:
ArXiv: 2111.04616


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