scholarly journals The classical exchange algebra ofAdS5×S5string theory

2009 ◽  
Vol 2009 (01) ◽  
pp. 021-021 ◽  
Author(s):  
Marc Magro
Keyword(s):  
Exchange Algebra

scholarly journals MULTIVALUED FIELDS ON THE COMPLEX PLANE AND BRAID GROUP STATISTICS

1994 ◽  
Vol 09 (03) ◽  
pp. 313-325 ◽  
Author(s):  
FRANCO FERRARI
Keyword(s):  
Riemann Surface ◽  
Complex Plane ◽  
Riemann Surfaces ◽  
Conformal Field Theories ◽  
Local Exchange ◽  
R Matrix ◽  
Conformal Field ◽  
Exchange Algebra ◽  
Braid Group Statistics ◽  
Nontrivial Topology

In this paper we study a class of theories of free particles on the complex plane satisfying a non-Abelian statistics. This kind of particles are generalizations of the anyons and are sometimes called plectons. The peculiarity of these theories is that they are associated to free conformal field theories defined on Riemann surfaces with a discrete and non-Abelian group of authomorphisms Dm. More explicitly, the plectons appear here as “induced vertex operators” that simulate, on the complex plane, the nontrivial topology of the Riemann surface. In order to express the local exchange algebra of the particles, one is led to introduce an R matrix satisfying a multiparameter generalization of the usual Yang-Baxter equations. It is interesting that analogous generalizations have already been investigated in connection with integrable models, in which the spectral parameter takes its values on a Riemann surface that is in many respects similar to the Riemann surfaces we are studying here. The explicit form of the R matrices mentioned above can be also used to define a multiparameter version of the quantum complex hyperplane.

BOSONIC SUPERCONFORMAL AFFINE TODA THEORY: EXCHANGE ALGEBRA AND DRESSING SYMMETRY

1993 ◽  
Vol 08 (21) ◽  
pp. 3773-3789 ◽  
Author(s):  
LIU CHAO ◽  
BO-YU HOU
Keyword(s):  
Semiclassical Limit ◽  
Group Symmetry ◽  
Hamiltonian Reduction ◽  
Classical Solutions ◽  
Conformal Invariant ◽  
Reconstruction Formula ◽  
R Matrix ◽  
Exchange Algebra ◽  
Integrable Field Theory ◽  
Integrable Field

We propose and investigate a new conformal invariant integrable field theory called bosonic superconformal affine Toda theory. This theory can be viewed either as the affine generalization of the so-called bosonic superconformal Toda theory studied by the authors sometime earlier, or as the generalization to the case of half-integer conformal weights of the conformal affine Toda theory, and can also be obtained from the Hamiltonian reduction of WZNW theory (with an affine WZNW group). The fundamental Poisson stracture is established in terms of the classical r matrix. Then the exchange algebra for the chiral vectors is obtained as well as the reconstruction formula for the classical solutions. The dressing transformations of the fundamental fields are found explicitly, and the Poisson-Lie structure of the dressing group is also constructed with the aid of classical exchange algebras, which turns out to be the semiclassical limit of the quantum affine group. The conformal breaking orbit of the model is also studied, which is called bosonic super loop Toda theory in the context. In addition, the quantum exchange relation and quantum group symmetry are discussed briefly.

SUPERSELECTION SECTORS WITH BRAID GROUP STATISTICS AND EXCHANGE ALGEBRAS II: GEOMETRIC ASPECTS AND CONFORMAL COVARIANCE

1992 ◽  
Vol 04 (spec01) ◽  
pp. 113-157 ◽  
Author(s):  
KLAUS FREDENHAGEN ◽  
KARL-HENNING REHREN ◽  
BERT SCHROER
Keyword(s):  
Braid Group ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Conformal Field Theories ◽  
Cpt Symmetry ◽  
Conformal Field ◽  
Exchange Algebra ◽  
Braid Group Statistics ◽  
Almost All ◽  
Conformal Covariance

The general theory of superselection sectors is shown to provide almost all the structure observed in two-dimensional conformal field theories. Its application to two-dimensional conformally covariant and three-dimensional Poincaré covariant theories yields a general spin-statistics connection previously encountered in more special situations. CPT symmetry can be shown also in the absence of local (anti-) commutation relations, if the braid group statistics is expressed in the form of an exchange algebra.

EXCHANGE ALGEBRA AND EXOTIC SUPERSYMMETRY IN THE CHIRAL POTTS MODEL

1990 ◽  
Vol 04 (05) ◽  
pp. 913-927 ◽  
Author(s):  
D. Bernard ◽  
V. Pasquier
Keyword(s):  
Potts Model ◽  
Point Of View ◽  
The Other ◽  
Chiral Potts Model ◽  
Exchange Algebra ◽  
Other Hand ◽  
S Matrix

We obtain an exchange algebra for the Chiral Potts model, the elements of which are linear in the parameters defining the rapidity curve. This enables us to connect the Chiral Potts model to a Uq(GL(2)) algebra. On the other hand, looking at the model from the S-matrix point of view relates it to a ZZ N generalisation of the supersymmetric algebra.

Classical r-matrix and exchange algebra in WZNW and Toda theories

1990 ◽  
Vol 244 (2) ◽  
pp. 227-234 ◽  
Author(s):  
J. Balog ◽  
L. Da̧browski ◽  
L. Fehér
Keyword(s):  
R Matrix ◽  
Exchange Algebra

scholarly journals FUSION AND BRAIDING IN W-ALGEBRA EXTENDED CONFORMAL THEORIES (II): GENERALIZATION TO CHIRAL SCREENED VERTEX OPERATORS LABELLED BY ARBITRARY YOUNG TABLEAUX

1990 ◽  
Vol 05 (10) ◽  
pp. 1881-1909 ◽  
Author(s):  
ADEL BILAL
Keyword(s):  
Potts Model ◽  
Braid Group ◽  
Simple Form ◽  
Group Representation ◽  
Symmetric Tensor ◽  
Vertex Operators ◽  
Young Tableaux ◽  
Exchange Algebra ◽  
Form Closure ◽  
Tensor Representations

In a previous work, we defined the chiral screened vertex operators of W-algebra extended conformal theories by fusion of elementary ones. After reviewing how to obtain the braid group representation matrices, realizing the exchange algebra for those chiral vertex operators corresponding to the symmetric tensor representations of An, we generalize our results to chiral screened vertex operators associated with arbitrary An representations. The fused braiding matrices for antisymmetric tensor screened vertex operators are computed explicitly and shown to have a very simple form. Closure of the exchange algebra in the general case is proved using the relation with the Boltzmann weights of the An face models. Since, in the unitary case, the W-algebras are realized as cosets ĝk⊕ĝ1/ĝk+1, the present results can also be reinterpreted in terms of fusion of braiding matrices of the ĝ WZW models. As an example, the simplest W-algebra extended theory, the 3-state Potts model, is discussed in some detail.

scholarly journals Symmetric space λ-model exchange algebra from 4d holomorphic Chern-Simons theory

2021 ◽  
Vol 2021 (12) ◽  
Author(s):  
David M. Schmidtt
Keyword(s):  
Symmetric Space ◽  
Sigma Model ◽  
Hamiltonian Formalism ◽  
Simons Theory ◽  
Symmetry Principle ◽  
R Matrix ◽  
Exchange Algebra ◽  
Coset Spaces ◽  
Chern Simons ◽  
Chern Simons Theory

Abstract We derive, within the Hamiltonian formalism, the classical exchange algebra of a lambda deformed string sigma model in a symmetric space directly from a 4d holomorphic Chern-Simons theory. The explicit forms of the extended Lax connection and R-matrix entering the Maillet bracket of the lambda model are explained from a symmetry principle. This approach, based on a gauge theory, may provide a mechanism for taming the non-ultralocality that afflicts most of the integrable string theories propagating in coset spaces.

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