Representations of the Nappi–Witten vertex operator algebra
| Autor: | William Stewart, Andrei Babichenko, David Ridout, Kazuya Kawasetsu |
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| Rok vydání: | 2021 |
| Předmět: |
High Energy Physics - Theory
Pure mathematics Conformal field theory Complex system FOS: Physical sciences Statistical and Nonlinear Physics Mathematical Physics (math-ph) Space (mathematics) Representation theory Logarithmic conformal field theory High Energy Physics::Theory High Energy Physics - Theory (hep-th) Vertex operator algebra Mathematics::Category Theory Mathematics - Quantum Algebra FOS: Mathematics Heisenberg group Quantum Algebra (math.QA) Affine transformation Mathematical Physics Mathematics |
| Zdroj: | Letters in Mathematical Physics. 111 |
| ISSN: | 1573-0530 0377-9017 |
| DOI: | 10.1007/s11005-021-01471-5 |
| Popis: | The Nappi-Witten model is a Wess-Zumino-Witten model in which the target space is the nonreductive Heisenberg group $H_4$. We consider the representation theory underlying this conformal field theory. Specifically, we study the category of weight modules, with finite-dimensional weight spaces, over the associated affine vertex operator algebra $\mathsf{H}_4$. In particular, we classify the irreducible $\mathsf{H}_4$-modules in this category and compute their characters. We moreover observe that this category is nonsemisimple, suggesting that the Nappi-Witten model is a logarithmic conformal field theory. 21 pages; introduction expanded, references added, minor notation changes |
| Databáze: | OpenAIRE |
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