scholarly journals On correlation functions of vertex operator algebras associated to Jordan algebras

2016 ◽  
Vol 468 ◽  
pp. 193-213
Author(s):  
Hongbo Zhao
Keyword(s):  
Vertex Operator ◽  
Correlation Functions ◽  
Operator Algebras ◽  
Jordan Algebras ◽  
Vertex Operator Algebras

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.

Cluster algebras based on vertex operator algebras

2016 ◽  
Vol 30 (28n29) ◽  
pp. 1640030
Author(s):  
Alexander Zuevsky
Keyword(s):  
Vertex Operator ◽  
Correlation Functions ◽  
Riemann Surfaces ◽  
Operator Algebras ◽  
Cluster Algebra ◽  
Cluster Algebras ◽  
Vertex Operator Algebras ◽  
Algebra Structure ◽  
Local Coordinates ◽  
Recursion Formulas

Starting from Zhu recursion formulas for correlation functions for vertex operator algebras with formal parameters associated to local coordinates around marked points on a Riemann surfaces, we introduce a cluster algebra structure over a noncommutative set of variables. Cluster elements and mutation rules are explicitly defined. In particular, we propose an elliptic version of vertex operator cluster algebras arising from correlation functions and Zhu reduction procedure for vertex operators on the torus.

scholarly journals Foliation of a space associated to vertex operator algebra

2021 ◽  
Author(s):  
A. Zuevsky
Keyword(s):  
Riemann Surface ◽  
Vertex Operator ◽  
Operator Algebra ◽  
Correlation Functions ◽  
Riemann Surfaces ◽  
Vertex Operator Algebra ◽  
Operator Algebras ◽  
Vertex Operator Algebras

In this paper, we construct the foliation of a space associated to correlation functions of vertex operator algebras, considered on Riemann surfaces. We prove that the computation of general genus g correlation functions determines a foliation on the space associated to these correlation functions a sewn Riemann surface. Certain further applications of the definition are proposed.

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
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