Twisted logarithmic modules of vertex algebras

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.

31 pages

References in corpus (3)

• Gromov--Witten theory of Fano orbifold curves, Gamma integral structures and ADE-Toda Hierarchies
• Generalized Vertex Algebras
• Jacobi Identity for Vertex Algebras in Higher Dimensions

Cited by in corpus (12)

• Twisted modules and $G$-equivariantization in logarithmic conformal field theory
• Self-dual and logarithmic representations of the twisted Heisenberg--Virasoro algebra at level zero
• A construction of lower-bounded generalized twisted modules for a grading-restricted vertex (super)algebra
• Additional symmetries of the extended bigraded Toda hierarchy
• Twisted logarithmic modules of lattice vertex algebras
• Twisted logarithmic modules of free field algebras
• Orbifolds of Lattice Vertex Algebras
• Logarithmic Vertex Algebras
• Twist vertex operators for twisted modules
• Twisted representations of vertex operator algebras associated to affine Lie algebras
• Lower-bounded and grading-restricted twisted modules for affine vertex (operator) algebras
• Representation theory of vertex operator algebras and orbifold conformal field theory