Logarithmic Vertex Algebras

Bojko N. Bakalov; Juan J. Villarreal

doi:10.1007/s00031-022-09759-z

Logarithmic Vertex Algebras

Bojko N. Bakalov, Juan J. Villarreal

Department of Mathematical Sciences

North Carolina State University

Research output: Contribution to journal › Article › peer-review

Abstract

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.

Original language	English
Journal	Transformation Groups
Early online date	9 Sept 2022
DOIs	https://doi.org/10.1007/s00031-022-09759-z
Publication status	E-pub ahead of print - 9 Sept 2022

Bibliographical note

Funding Information:
The first author was supported in part by a Simons Foundation grant 584741.

Keywords

Logarithmic conformal field theory
Vertex algebra
Virasoro algebra

ASJC Scopus subject areas

Algebra and Number Theory
Geometry and Topology

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10.1007/s00031-022-09759-z

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Y1 - 2022/9/9

N2 - 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.

AB - 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.

KW - Logarithmic conformal field theory

KW - Vertex algebra

KW - Virasoro algebra

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Logarithmic Vertex Algebras

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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