scholarly journals Exceptional vertex operator algebras and the Virasoro algebra

2009 ◽  
pp. 213-225 ◽  
Author(s):  
Michael P. Tuite
Keyword(s):  
Vertex Operator ◽  
Operator Algebras ◽  
Virasoro Algebra ◽  
Vertex Operator Algebras ◽  
Exceptional Vertex

scholarly journals Formal Calculus and Umbral Calculus

10.37236/367 ◽  
2010 ◽  
Vol 17 (1) ◽  
Author(s):  
Thomas J. Robinson
Keyword(s):  
Vertex Operator ◽  
Operator Algebras ◽  
Virasoro Algebra ◽  
Umbral Calculus ◽  
Vertex Operator Algebras ◽  
Composite Function ◽  
Formal Calculus ◽  
Higher Derivatives ◽  
Basic Facts ◽  
Derivatives Of

We use the viewpoint of the formal calculus underlying vertex operator algebra theory to study certain aspects of the classical umbral calculus. We begin by calculating the exponential generating function of the higher derivatives of a composite function, following a very short proof which naturally arose as a motivating computation related to a certain crucial "associativity" property of an important class of vertex operator algebras. Very similar (somewhat forgotten) proofs had appeared by the 19-th century, of course without any motivation related to vertex operator algebras. Using this formula, we derive certain results, including especially the calculation of certain adjoint operators, of the classical umbral calculus. This is, roughly speaking, a reversal of the logical development of some standard treatments, which have obtained formulas for the higher derivatives of a composite function, most notably Faà di Bruno's formula, as a consequence of umbral calculus. We also show a connection between the Virasoro algebra and the classical umbral shifts. This leads naturally to a more general class of operators, which we introduce, and which include the classical umbral shifts as a special case. We prove a few basic facts about these operators.

scholarly journals Vertex operator algebras associated to the Virasoro algebra over an arbitrary field

2015 ◽  
Vol 368 (7) ◽  
pp. 5177-5196 ◽  
Author(s):  
Chongying Dong ◽  
Li Ren
Keyword(s):  
Vertex Operator ◽  
Operator Algebras ◽  
Virasoro Algebra ◽  
Vertex Operator Algebras ◽  
Arbitrary Field

Vertex Operator Algebras and Moonshine: A Survey

2018 ◽  
Author(s):  
Chongying Dong ◽  
Geoffrey Mason
Keyword(s):  
Vertex Operator ◽  
Operator Algebras ◽  
Vertex Operator Algebras

scholarly journals W algebras, cosets and VOAs for 4d $$ \mathcal{N} $$ = 2 SCFTs from M5 branes

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Dan Xie ◽  
Wenbin Yan
Keyword(s):  
Vertex Operator ◽  
Operator Algebras ◽  
Nilpotent Orbit ◽  
Vertex Operator Algebras ◽  
Flavor Symmetries ◽  
Conformal Embedding

Abstract We identify vertex operator algebras (VOAs) of a class of Argyres-Douglas (AD) matters with two types of non-abelian flavor symmetries. They are the W algebras defined using nilpotent orbit with partition [qm, 1s]. Gauging above AD matters, we can find VOAs for more general $$ \mathcal{N} $$ N = 2 SCFTs engineered from 6d (2, 0) theories. For example, the VOA for general (AN − 1, Ak − 1) theory is found as the coset of a collection of above W algebras. Various new interesting properties of 2d VOAs such as level-rank duality, conformal embedding, collapsing levels, coset constructions for known VOAs can be derived from 4d theory.

Z2k-code vertex operator algebras

2021 ◽  
Vol 573 ◽  
pp. 451-475
Author(s):  
Hiromichi Yamada ◽  
Hiroshi Yamauchi
Keyword(s):  
Vertex Operator ◽  
Operator Algebras ◽  
Vertex Operator Algebras

scholarly journals Construction and classification of holomorphic vertex operator algebras

2020 ◽  
Vol 2020 (759) ◽  
pp. 61-99 ◽  
Author(s):  
Jethro van Ekeren ◽  
Sven Möller ◽  
Nils R. Scheithauer
Keyword(s):  
Vertex Operator ◽  
Operator Algebras ◽  
Central Charge ◽  
Field Theories ◽  
Vertex Operator Algebras ◽  
Conformal Field Theories ◽  
Cyclic Groups ◽  
Conformal Field

AbstractWe develop an orbifold theory for finite, cyclic groups acting on holomorphic vertex operator algebras. Then we show that Schellekens’ classification of {V_{1}}-structures of meromorphic conformal field theories of central charge 24 is a theorem on vertex operator algebras. Finally, we use these results to construct some new holomorphic vertex operator algebras of central charge 24 as lattice orbifolds.

scholarly journals VIRASORO CORRELATION FUNCTIONS FOR VERTEX OPERATOR ALGEBRAS

2012 ◽  
Vol 23 (10) ◽  
pp. 1250106 ◽  
Author(s):  
DONNY HURLEY ◽  
MICHAEL P. TUITE
Keyword(s):  
Graph Theory ◽  
Vertex Operator ◽  
Generating Functions ◽  
Operator Algebra ◽  
Correlation Functions ◽  
Vertex Operator Algebra ◽  
Operator Algebras ◽  
Vertex Operator Algebras ◽  
Genus Zero ◽  
Genus One

We consider all genus zero and genus one correlation functions for the Virasoro vacuum descendants of a vertex operator algebra. These are described in terms of explicit generating functions that can be combinatorially expressed in terms of graph theory related to derangements in the genus zero case and to partial permutations in the genus one case.

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