scholarly journals Vertex operator representation of the soliton tau functions in the An(1) Toda models by dressing transformations

1998 ◽  
Vol 39 (10) ◽  
pp. 5337-5363
Author(s):  
H. Belich ◽  
G. Cuba ◽  
R. Paunov
Keyword(s):  
Vertex Operator ◽  
Operator Representation ◽  
Tau Functions ◽  
Vertex Operator Representation

scholarly journals A vertex operator representation of solutions to the Gurevich-Zybin hydrodynamical equation

2013 ◽  
Vol 33 (1) ◽  
pp. 139
Author(s):  
Yarema A. Prykarpatsky ◽  
Denis Blackmore ◽  
Jolanta Golenia ◽  
Anatoliy K. Prykarpatsky
Keyword(s):  
Vertex Operator ◽  
Hydrodynamical Equation ◽  
Operator Representation ◽  
Representation Of Solutions ◽  
Vertex Operator Representation

VERTEX OPERATOR REPRESENTATION OF OSp(M|N)(1)

1988 ◽  
Vol 03 (11) ◽  
pp. 2545-2566 ◽  
Author(s):  
L. FRAPPAT
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
String Theory ◽  
Vertex Operator ◽  
Vertex Operators ◽  
Operator Representation ◽  
Conformal Field ◽  
Vertex Operator Representation

Using the boson-fermion equivalence in 2-d conformal field theory and the boson-boson equivalence of the superconformal bosonic ghost fields of the string theory, we construct a level k=+1 representation of the affine superalgebra OSp (M|N)(1) in terms of vertex operators.

scholarly journals ANYONS IN A MAGNETIC FIELD: LANDAU LEVELS AND VERTEX OPERATOR REPRESENTATION

1991 ◽  
Vol 05 (10) ◽  
pp. 1675-1684 ◽  
Author(s):  
Gerald V. Dunne ◽  
Alberto Lerda ◽  
Carlo A. Trugenberger
Keyword(s):  
Magnetic Field ◽  
Angular Momentum ◽  
External Magnetic Field ◽  
Vertex Operator ◽  
Ground State ◽  
Landau Levels ◽  
Vertex Operators ◽  
Many Body ◽  
Natural Representation ◽  
Operator Representation

We construct exact many-body eigenstates of both energy and angular momentum for the N-anyon problem in an external magnetic field. Such states span the full ground-state eigenspace and have a natural representation in terms of the Fubini-Veneziano vertex operators of string theory.

scholarly journals On tau-functions for the KdV hierarchy

2021 ◽  
Vol 27 (1) ◽  
Author(s):  
Boris Dubrovin ◽  
Di Yang ◽  
Don Zagier
Keyword(s):  
Tau Functions ◽  
Kdv Hierarchy

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 Padé approximants on Riemann surfaces and KP tau functions

2021 ◽  
Vol 11 (4) ◽  
Author(s):  
Marco Bertola
Keyword(s):  
Riemann Surface ◽  
Riemann Surfaces ◽  
Hilbert Problem ◽  
Line Bundles ◽  
Fixed Degree ◽  
Tau Function ◽  
Tau Functions ◽  
Deformation Parameters ◽  
Higher Genus ◽  
Geometric Solutions

AbstractThe paper has two relatively distinct but connected goals; the first is to define the notion of Padé approximation of Weyl–Stiltjes transforms on an arbitrary compact Riemann surface of higher genus. The data consists of a contour in the Riemann surface and a measure on it, together with the additional datum of a local coordinate near a point and a divisor of degree g. The denominators of the resulting Padé-like approximation also satisfy an orthogonality relation and are sections of appropriate line bundles. A Riemann–Hilbert problem for a square matrix of rank two is shown to characterize these orthogonal sections, in a similar fashion to the ordinary orthogonal polynomial case. The second part extends this idea to explore its connection to integrable systems. The same data can be used to define a pairing between two sequences of line bundles. The locus in the deformation space where the pairing becomes degenerate for fixed degree coincides with the zeros of a “tau” function. We show how this tau function satisfies the Kadomtsev–Petviashvili hierarchy with respect to either deformation parameters, and a certain modification of the 2-Toda hierarchy when considering the whole sequence of tau functions. We also show how this construction is related to the Krichever construction of algebro-geometric solutions.

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.

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