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Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.
I have expanded vertex operator algebra (more references, more items in the Properties-section) in partial support to a TP.SE answer that I posted here
added to the References at vertex operator algebra a pointer to their formalization as factorization algebras of observables.
I added two references at vertex operator algebra, in the bibliography section on deformations.
added pointer to today’s
added publication data to:
This triple of independent preprints appears today — apparently the groups realized they all have related results and coordinated to submit on the same day:
Philip Boyle Smith, Ying-Hsuan Lin, Yuji Tachikawa, Yunqin Zheng, Classification of chiral fermionic CFTs of central charge $\leq 16$ [arXiv:2303.16917]
Brandon C. Rayhaun, Bosonic Rational Conformal Field Theories in Small Genera, Chiral Fermionization, and Symmetry/Subalgebra Duality [arXiv:2303.16921]
Gerald Höhn, Sven Möller, Classification of Self-Dual Vertex Operator Superalgebras of Central Charge at Most 24 [arXiv:2303.17190]
So I also added pointer to these precursors:
Adrian Norbert Schellekens, Meromorphic $c = 24$ Conformal Field Theories, Commun. Math. Phys. 153 (1993) 159-186 [doi:10.1007/BF02099044]
Chongying Dong, Geoffrey Mason, Holomorphic Vertex Operator Algebras of Small Central Charges, Pacific Journal of Mathematics 213 2 (2004) 253–266 [arXiv:math/0203005, doi:10.2140/pjm.2004.213.253]
For Rayhaun’s paper arXiv now produces the following message, which as far as I remember, is the first one when arXiv flat out refuses to produce a PDF:
PDF unavailable …
Our automated source to PDF conversion system has failed to produce PDF for the paper: 2303.16921.
Return to the abstract for an alternative link to the source, or to find an email address to contact the author.
For help regarding the automated source to PDF system, please contact help@arxiv.org, remembering to specify the problematic archive and paper number.
It looks like in their constant pursuit of various new features (“arXiv Labs”) they neglected their core technology…
(Added into the literature)
Another approach to the definition
We encapsulate the basic notions of the theory of vertex algebras into the construction of a comonad on an appropriate category of formal distributions. Vertex algebras are recovered as coalgebras over this comonad.
Edit: this guy is giving a talk tomorrow, Wed 2023/08/16 (i am not sure about zoom link yet, see https://researchseminars.org/talk/HKUST-AG/11):
Chiral homology, the Zhu algebra, and Rogers-Ramanujan
Jethro van Ekeren (Instituto de Matemática Pura e Aplicada (IMPA))
https://researchseminars.org/seminar/HKUST-AG
Lecture held in Room 5506, Hong Kong University of Science and Technology (HKUST)
Abstract: Graded dimensions of rational vertex algebras are modular functions. The proof of this celebrated theorem by Y. Zhu centres on geometric objects attached to elliptic curves known as conformal blocks, and their behaviour in the limit as the underlying curve becomes singular. In this limit, roughly speaking, conformal blocks pass to the degree zero Hochschild homology of Zhu’s associative algebra. On the other hand, conformal blocks have been interpreted by Beilinson and Drinfeld as the degree zero component of a theory of chiral homology. It is therefore natural to wonder if the relationship extends to higher homological degrees. We are indeed able to extend this story to homological degree 1 for classically free vertex algebras, and in the process we discover relations with objects of number theory such as the Rogers-Ramanujan identity and its generalisations. This is joint work with R. Heluani and G. Andrews.
Surely, I was not sure how to classify.
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