Logarithmic Vertex Algebras

We introduce and study the notion of a logarithmic vertex algebra, which is a vertex algebra with logarithmic singularities in the operator product expansion of quantum fields; thus providing a rigorous formulation of the algebraic properties of quantum fields in logarithmic conformal field theory....

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Bibliographic Details
Published in:arXiv.org 2021-08
Main Authors: Bakalov, Bojko, Villarreal, Juan J
Format: Article
Language:English
Subjects:
Algebra
Existence theorems
Field theory
Online Access:Get full text
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Summary:We introduce and study the notion of a logarithmic vertex algebra, which is a vertex algebra with logarithmic singularities in the operator product expansion of quantum fields; thus providing a rigorous formulation of the algebraic properties of quantum fields in logarithmic conformal field theory. We develop a framework that allows many results about vertex algebras to be extended to logarithmic vertex algebras, including in particular the Borcherds identity and Kac Existence Theorem. Several examples are investigated in detail, and they exhibit some unexpected new features that are peculiar to the logarithmic case.
ISSN:2331-8422
DOI:10.48550/arxiv.2107.10206