Twisted logarithmic modules of lattice vertex algebras

TL;DR

This paper studies twisted logarithmic modules of lattice vertex algebras, connecting their classification to modules over a specific semidirect product group, advancing understanding in logarithmic conformal field theory.

Contribution

It reduces the classification of twisted logarithmic modules of lattice vertex algebras to modules over a particular semidirect product group, providing a new structural insight.

Findings

Classification of twisted logarithmic modules is reduced to group module classification.

Identification of the relevant group as a semidirect product of a Heisenberg group and a central extension.

Links between twisted modules and logarithmic conformal field theory are clarified.

Abstract

Twisted modules over vertex algebras formalize the relations among twisted vertex operators and have applications to conformal field theory and representation theory. A recent generalization, called twisted logarithmic module, involves the logarithm of the formal variable and is related to logarithmic conformal field theory. We investigate twisted logarithmic modules of lattice vertex algebras, reducing their classification to the classification of modules over a certain group. This group is a semidirect product of a discrete Heisenberg group and a central extension of the additive group of the lattice.