2022 article
Logarithmic Vertex Algebras
Bakalov, B. N., & Villarreal, J. J. (2022, September 9). TRANSFORMATION GROUPS.
author keywords: Logarithmic conformal field theory; Vertex algebra; Virasoro algebra
open access via arxiv.org (repository)
Source: Web Of Science
Added: September 19, 2022
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.