Twisted Logarithmic Modules of Vertex Algebras

2015/04/24 by Bojko Bakalov · 1 citation
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Affine Lie algebra #Affine transformation #Algebra over a field #Algebraic structures and combinatorial models #Automorphism #Commutator #Conformal field theory #Conformal map #Current algebra #Discrete mathematics #Jordan algebra #Lie conformal algebra #Logarithm #Mathematical analysis #Mathematics #Nonlinear Waves and Solitons #Pure mathematics #Vertex (graph theory) #Vertex operator algebra #math.QA #msc:17B69 #msc:81R10

paper · pdf · doi:10.1007/s00220-015-2503-9

published as Comm. Math. Phys. 345 (2016), no. 1, 355-383 · 31 pages

arxiv created 2015/04/24 · openalex publication_date 2015/11/25 · arxiv updated 2016/06/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

Motivated by logarithmic conformal field theory and Gromov-Witten theory, we introduce a notion of a twisted module of a vertex algebra under an arbitrary (not necessarily semisimple) automorphism. Its main feature is that the twisted fields involve the logarithm of the formal variable. We develop the theory of such twisted modules and, in particular, derive a Borcherds identity and commutator formula for them. We investigate in detail the examples of affine and Heisenberg vertex algebras.

Citations

• Generalized Vertex Algebras
• Infinite conformal symmetry in two-dimensional quantum field theory
• -constraints for the total descendant potential of a simple singularity
• Local systems of vertex operators, vertex superalgebras and modules
• Strings on orbifolds
• Vertex algebras, Kac-Moody algebras, and the Monster
• Conformal Field Theory

Cited by

• Coupling a vertex algebra to a large center