Twisted Chiral Algebras of Class S and Mixed Feigin-Frenkel Gluing.

Autor: Beem C; Mathematical Institute, University of Oxford, Woodstock Road, Oxford, OX2 6GG UK., Nair S; Mathematical Institute, University of Oxford, Woodstock Road, Oxford, OX2 6GG UK.
Jazyk: angličtina
Zdroj: Communications in mathematical physics [Commun Math Phys] 2023; Vol. 399 (1), pp. 295-366. Date of Electronic Publication: 2022 Nov 11.
DOI: 10.1007/s00220-022-04556-x
Abstrakt: The correspondence between four-dimensional N = 2 superconformal field theories and vertex operator algebras, when applied to theories of class S , leads to a rich family of VOAs that have been given the monicker chiral algebras of class S . A remarkably uniform construction of these vertex operator algebras has been put forward by Tomoyuki Arakawa in Arakawa (Chiral algebras of class S 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 g , and applies equally well regardless of whether g 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 S 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 S with outer automorphism twist lines. We show that our definition passes some consistency checks and point out some important open problems.
Competing Interests: Conflict of interestsThe authors have no competing interests to declare that are relevant to the content of this article.
(© The Author(s) 2022.)
Databáze: MEDLINE
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