Admissible-level $\mathfrak{sl}_3$ minimal models
| Autor: | Kazuya Kawasetsu, David Ridout, Simon Wood |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2021 |
| Předmět: |
High Energy Physics - Theory
High Energy Physics - Theory (hep-th) Mathematics - Quantum Algebra FOS: Mathematics Quantum Algebra (math.QA) FOS: Physical sciences Statistical and Nonlinear Physics Mathematical Physics (math-ph) Representation Theory (math.RT) Mathematical Physics Mathematics - Representation Theory |
| Popis: | The first part of this work uses the algorithm recently detailed in arXiv:1906.02935 to classify the irreducible weight modules of the minimal model vertex operator algebra $L_k(\mathfrak{sl}_3)$, when the level $k$ is admissible. These are naturally described in terms of families parametrised by up to two complex numbers. We also determine the action of the relevant group of automorphisms of $\hat{\mathfrak{sl}}_3$ on their isomorphism classes and compute explicitly the decomposition into irreducibles when a given family's parameters are permitted to take certain limiting values. Along with certain character formulae, previously established in arXiv:2003.10148, these results form the input data required by the standard module formalism to consistently compute modular transformations and, assuming the validity of a natural conjecture, the Grothendieck fusion coefficients of the admissible-level $\mathfrak{sl}_3$ minimal models. The second part of this work applies the standard module formalism to compute these explicitly when $k=-\frac32$. We expect that the methodology developed here will apply in much greater generality. 34 pages, 5 figures; v2: 37 pages, 5 figures, updated refs, added explanations and discussed relationship with other interesting VOAs |
| Databáze: | OpenAIRE |
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