An equivalence of two constructions of permutation-twisted modules for lattice vertex operator algebras

An Equivalence of Two Constructions of Permutation-twisted Modules for Lattice Vertex Operator Algebras

The problem of constructing twisted modules for a vertex operator algebra and an automorphism has been solved in particular in two contexts. One of these two constructions is that initiated by the third author in the case of a lattice vertex operator algebra and an automorphism arising from an arbitrary lattice isometry. This construction, from a physical point of view, is related to the space-...

Twisted modules for vertex operator algebras

In this contribution, I explain the general principles of twisted modules for vertex operator algebras in its powerful formulation using formal series, and derive new general relations satisfied by twisted and non-twisted vertex operators. I prove new “equivalence” and “construction” theorems, identifying a very restricted set of sufficient conditions in order to have a twisted module for a ver...

Twisted Modules over Lattice Vertex Algebras

A vertex algebra is essentially the same as a chiral algebra in conformal field theory [2, 10]. Vertex algebras arose naturally in the representation theory of infinite-dimensional Lie algebras and in the construction of the “moonshine module” for the Monster finite simple group [3, 9]. If V is a vertex algebra and Γ is a finite group of automorphisms of V , the subalgebra V Γ of Γ-invariant el...

Some Twisted Modules for Framed Vertex Operator Algebras

Twisted modules for vertex operator algebras and Bernoulli polynomials

Using general principles of the theory of vertex operator algebras and their twisted modules, we obtain a bosonic, twisted construction of a certain central extension of a Lie algebra of differential operators on the circle, for an arbitrary twisting automorphism. The construction involves the Bernoulli polynomials in a fundamental way. This is explained through results in the general theory of...