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Twisted Chiral Algebras of Class [Formula: see text] and Mixed Feigin–Frenkel Gluing
The correspondence between four-dimensional [Formula: see text] superconformal field theories and vertex operator algebras, when applied to theories of class [Formula: see text] , leads to a rich family of VOAs that have been given the monicker chiral algebras of class [Formula: see text] . A remark...
Autores principales: | , |
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Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
Springer Berlin Heidelberg
2022
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Materias: | |
Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10050081/ https://www.ncbi.nlm.nih.gov/pubmed/37009431 http://dx.doi.org/10.1007/s00220-022-04556-x |
Sumario: | The correspondence between four-dimensional [Formula: see text] superconformal field theories and vertex operator algebras, when applied to theories of class [Formula: see text] , leads to a rich family of VOAs that have been given the monicker chiral algebras of class [Formula: see text] . A remarkably uniform construction of these vertex operator algebras has been put forward by Tomoyuki Arakawa in Arakawa (Chiral algebras of class [Formula: see text] and Moore–Tachikawa symplectic varieties, 2018. arXiv:1811.01577 [math.RT]). The construction of Arakawa (2018) takes as input a choice of simple Lie algebra [Formula: see text] , and applies equally well regardless of whether [Formula: see text] is simply laced or not. In the non-simply laced case, however, the resulting VOAs do not correspond in any clear way to known four-dimensional theories. On the other hand, the standard realisation of class [Formula: see text] theories involving non-simply laced symmetry algebras requires the inclusion of outer automorphism twist lines, and this requires a further development of the approach of Arakawa (2018). In this paper, we give an account of those further developments and propose definitions of most chiral algebras of class [Formula: see text] with outer automorphism twist lines. We show that our definition passes some consistency checks and point out some important open problems. |
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