A Lax representation for the vertex operator and the central extension

1995 ◽  
Vol 171 (3) ◽  
pp. 547-588 ◽  
Author(s):  
M. Adler ◽  
T. Shiota ◽  
P. van Moerbeke
Keyword(s):  
Vertex Operator ◽  
Central Extension ◽  
Lax Representation

scholarly journals TWISTED VERTEX OPERATORS AND BERNOULLI POLYNOMIALS

2006 ◽  
Vol 08 (02) ◽  
pp. 247-307 ◽  
Author(s):  
B. DOYON ◽  
J. LEPOWSKY ◽  
A. MILAS
Keyword(s):  
Vertex Operator ◽  
Operator Algebra ◽  
Central Extension ◽  
Vertex Operator Algebra ◽  
Differential Operators ◽  
Operator Algebras ◽  
Bernoulli Polynomials ◽  
Vertex Operator Algebras ◽  
Vertex Operators ◽  
Special Case

Using general principles in 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. We develop new identities and principles in the theory of vertex operator algebras and their twisted modules, and explain the construction by applying general results, including an identity that we call modified weak associativity, to the Heisenberg vertex operator algebra. This paper gives proofs and further explanations of results announced earlier. It is a generalization to twisted vertex operators of work announced by the second author some time ago, and includes as a special case the proof of the main results of that work.

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 Intertwining operator and integrable hierarchies from topological strings

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Jean-Emile Bourgine
Keyword(s):  
Topological Strings ◽  
Vertex Operator ◽  
Integrable Hierarchies ◽  
Kp Hierarchy ◽  
Tau Function ◽  
Time Deformation ◽  
Toroidal Algebra ◽  
Crystal Model ◽  
Melting Crystal ◽  
Definition Of

Abstract In [1], Nakatsu and Takasaki have shown that the melting crystal model behind the topological strings vertex provides a tau-function of the KP hierarchy after an appropriate time deformation. We revisit their derivation with a focus on the underlying quantum W1+∞ symmetry. Specifically, we point out the role played by automorphisms and the connection with the intertwiner — or vertex operator — of the algebra. This algebraic perspective allows us to extend part of their derivation to the refined melting crystal model, lifting the algebra to the quantum toroidal algebra of $$ \mathfrak{gl} $$ gl (1) (also called Ding-Iohara-Miki algebra). In this way, we take a first step toward the definition of deformed hierarchies associated to A-model refined topological strings.

scholarly journals Relating the b ghost and the vertex operators of the pure spinor superstring

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Osvaldo Chandia ◽  
Brenno Carlini Vallilo
Keyword(s):  
Vertex Operator ◽  
Bosonic String ◽  
Vertex Operators ◽  
Pure Spinor ◽  
Double Pole ◽  
Lorenz Gauge

Abstract The OPE between the composite b ghost and the unintegrated vertex operator for massless states of the pure spinor superstring is computed and shown to reproduce the structure of the bosonic string result. The double pole vanishes in the Lorenz gauge and the single pole is shown to be equal to the corresponding integrated vertex operator.

scholarly journals Stress-energy tensor correlators from the world-sheet

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Hanno Bertle ◽  
Andrea Dei ◽  
Matthias R. Gaberdiel
Keyword(s):  
Vertex Operator ◽  
Energy Tensor ◽  
Stress Energy Tensor ◽  
World Sheet ◽  
Stress Energy ◽  
The World

Abstract The large N limit of symmetric orbifold theories was recently argued to have an AdS/CFT dual world-sheet description in terms of an sl(2, ℝ) WZW model. In previous work the world-sheet state corresponding to the symmetric orbifold stress-energy tensor was identified. We calculate certain 2- and 3-point functions of the corresponding vertex operator on the world-sheet, and demonstrate that these amplitudes reproduce exactly what one expects from the dual symmetric orbifold perspective.

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