Classification of screening systems for lattice vertex operator algebras

Katrina Barron, Nathan Vander Werf

Research output: Contribution to journalArticle

Abstract

We study and classify systems of certain screening operators arising in a generalized vertex operator algebra, or more generally an abelian intertwining algebra with an associated vertex operator (super)algebra. Screening pairs arising from weight one primary vectors acting commutatively on a lattice vertex operator algebra (the vacuum module) are classified into four general types; one type of which has been shown to play an important role in the construction and study of certain important families of W-vertex algebras. These types of screening pairs which we go on to study in detail through the notion of a system of screeners are lattice elements or “screening momenta” which give rise to screening pairs. We classify screening systems for all positive definite integral lattices of rank two, and for all positive definite even lattices of arbitrary rank when these lattices are generated by a screening system.

Original languageEnglish (US)
JournalLetters in Mathematical Physics
DOIs
StateAccepted/In press - Jan 1 2019

Fingerprint

Vertex Operator Algebras
Screening
algebra
apexes
screening
operators
Positive definite
Classify
Vertex Algebra
Definite integral
Vertex Operators
Superalgebra
Vacuum
Momentum
modules
momentum
Module
vacuum
Algebra
Arbitrary

Keywords

  • Conformal field theory
  • Screening operators
  • Vertex operator algebras

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

Cite this

Classification of screening systems for lattice vertex operator algebras. / Barron, Katrina; Vander Werf, Nathan.

In: Letters in Mathematical Physics, 01.01.2019.

Research output: Contribution to journalArticle

@article{f2d778b36c9d4be9860db070724f7a37,
title = "Classification of screening systems for lattice vertex operator algebras",
abstract = "We study and classify systems of certain screening operators arising in a generalized vertex operator algebra, or more generally an abelian intertwining algebra with an associated vertex operator (super)algebra. Screening pairs arising from weight one primary vectors acting commutatively on a lattice vertex operator algebra (the vacuum module) are classified into four general types; one type of which has been shown to play an important role in the construction and study of certain important families of W-vertex algebras. These types of screening pairs which we go on to study in detail through the notion of a system of screeners are lattice elements or “screening momenta” which give rise to screening pairs. We classify screening systems for all positive definite integral lattices of rank two, and for all positive definite even lattices of arbitrary rank when these lattices are generated by a screening system.",
keywords = "Conformal field theory, Screening operators, Vertex operator algebras",
author = "Katrina Barron and Nathan Vander Werf",
year = "2019",
month = "1",
day = "1",
doi = "10.1007/s11005-019-01161-3",
language = "English (US)",
journal = "Letters in Mathematical Physics",
issn = "0377-9017",
publisher = "Springer Netherlands",

}

TY - JOUR

T1 - Classification of screening systems for lattice vertex operator algebras

AU - Barron, Katrina

AU - Vander Werf, Nathan

PY - 2019/1/1

Y1 - 2019/1/1

N2 - We study and classify systems of certain screening operators arising in a generalized vertex operator algebra, or more generally an abelian intertwining algebra with an associated vertex operator (super)algebra. Screening pairs arising from weight one primary vectors acting commutatively on a lattice vertex operator algebra (the vacuum module) are classified into four general types; one type of which has been shown to play an important role in the construction and study of certain important families of W-vertex algebras. These types of screening pairs which we go on to study in detail through the notion of a system of screeners are lattice elements or “screening momenta” which give rise to screening pairs. We classify screening systems for all positive definite integral lattices of rank two, and for all positive definite even lattices of arbitrary rank when these lattices are generated by a screening system.

AB - We study and classify systems of certain screening operators arising in a generalized vertex operator algebra, or more generally an abelian intertwining algebra with an associated vertex operator (super)algebra. Screening pairs arising from weight one primary vectors acting commutatively on a lattice vertex operator algebra (the vacuum module) are classified into four general types; one type of which has been shown to play an important role in the construction and study of certain important families of W-vertex algebras. These types of screening pairs which we go on to study in detail through the notion of a system of screeners are lattice elements or “screening momenta” which give rise to screening pairs. We classify screening systems for all positive definite integral lattices of rank two, and for all positive definite even lattices of arbitrary rank when these lattices are generated by a screening system.

KW - Conformal field theory

KW - Screening operators

KW - Vertex operator algebras

UR - http://www.scopus.com/inward/record.url?scp=85062954473&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85062954473&partnerID=8YFLogxK

U2 - 10.1007/s11005-019-01161-3

DO - 10.1007/s11005-019-01161-3

M3 - Article

AN - SCOPUS:85062954473

JO - Letters in Mathematical Physics

JF - Letters in Mathematical Physics

SN - 0377-9017

ER -