Logarithmic Vertex Algebras

Bojko N. Bakalov, Juan J. Villarreal

Research output: Contribution to journalArticlepeer-review


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 languageEnglish
JournalTransformation Groups
Early online date9 Sept 2022
Publication statusE-pub ahead of print - 9 Sept 2022


  • Logarithmic conformal field theory
  • Vertex algebra
  • Virasoro algebra

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Geometry and Topology


Dive into the research topics of 'Logarithmic Vertex Algebras'. Together they form a unique fingerprint.

Cite this