Logarithmic Vertex Algebras

TL;DR

This paper introduces logarithmic vertex algebras, extending classical vertex algebra theory to include logarithmic singularities, and explores their properties and examples in the context of logarithmic conformal field theory.

Contribution

It provides a rigorous framework for logarithmic vertex algebras, extending key results like Borcherds identity and Kac Existence Theorem to this new setting.

Findings

Development of a formal framework for logarithmic vertex algebras

Extension of fundamental vertex algebra results to the logarithmic case

Identification of novel features unique to logarithmic vertex algebras

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.