Super Vertex Algebras, Meromorphic Jacobi Forms and Umbral Moonshine
| Autor: | Andrew O'Desky, John F. R. Duncan |
|---|---|
| Rok vydání: | 2017 |
| Předmět: |
High Energy Physics - Theory
Vertex (graph theory) Pure mathematics Algebra and Number Theory 010308 nuclear & particles physics 010102 general mathematics Modular form Coxeter group FOS: Physical sciences 01 natural sciences Lie conformal algebra Algebra Operator algebra Vertex operator algebra High Energy Physics - Theory (hep-th) 0103 physical sciences FOS: Mathematics 0101 mathematics Representation Theory (math.RT) Mathematics - Representation Theory Umbral moonshine Mathematics Meromorphic function |
| DOI: | 10.48550/arxiv.1705.09333 |
| Popis: | The vector-valued mock modular forms of umbral moonshine may be repackaged into meromorphic Jacobi forms of weight one. In this work we constructively solve two cases of the meromorphic module problem for umbral moonshine. Specifically, for the type A Niemeier root systems with Coxeter numbers seven and thirteen, we construct corresponding bigraded super vertex operator algebras, equip them with actions of the corresponding umbral groups, and verify that the resulting trace functions on canonically twisted modules recover the meromorphic Jacobi forms that are specified by umbral moonshine. We also obtain partial solutions to the meromorphic module problem for the type A Niemeier root systems with Coxeter numbers four and five, by constructing super vertex operator algebras that recover the meromorphic Jacobi forms attached to maximal subgroups of the corresponding umbral groups. Comment: 25 pages |
| Databáze: | OpenAIRE |
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