Twist vertex operators for twisted modules

TL;DR

This paper develops the theory of twist vertex operators for twisted modules in vertex (super)algebras, establishing key properties that facilitate explicit module construction.

Contribution

It introduces and proves fundamental properties of twist vertex operators, enabling new methods for constructing twisted modules.

Findings

Proved duality, weak associativity, and Jacobi identity for twist vertex operators.

Established convergence and commutativity properties for multiple operators.

Provided a foundation for explicit twisted module construction.

Abstract

We introduce and study twist vertex operators for a (lower-bounded generalized) twisted modules for a grading-restricted vertex (super)algebra. We prove duality, weak associativity, a Jacobi identity, a generalized commutator formula, generalized weak commutativity, and convergence and commutativity for products of more than two operators involving twist vertex operators. These properties of twist vertex operators play an important role in the author's recent general, direct and explicit construction of (lower-bounded generalized) twisted modules.