Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2001-03-15
Rev.Math.Phys. 16 (2004) 679-808
Physics
High Energy Physics
High Energy Physics - Theory
165 pages, LaTeX, many improvements, some new results; e.g. we show the equivalence of our q-current algebra and that of Reshe
Scientific paper
A dynamical system is canonically associated to every Drinfeld double of any affine Kac-Moody group. The choice of the affine Lu-Weinstein-Soibelman double gives a smooth one-parameter deformation of the standard WZW model. In particular, the worldsheet and the target of the classical version of the deformed theory are the ordinary smooth manifolds. The quasitriangular WZW model is exactly solvable and it admits the chiral decomposition.Its classical action is not invariant with respect to the left and right action of the loop group, however it satisfies the weaker condition of the Poisson-Lie symmetry. The structure of the deformed WZW model is characterized by several ordinary and dynamical r-matrices with spectral parameter. They describe the q-deformed current algebras, they enter the definition of q-primary fields and they characterize the quasitriangular exchange (braiding) relations. Remarkably, the symplectic structure of the deformed chiral WZW theory is cocharacterized by the same elliptic dynamical r-matrix that appears in the Bernard generalization of the Knizhnik-Zamolodchikov equation, with q entering the modular parameter of the Jacobi theta functions. This reveals a tantalizing connection between the classical q-deformed WZW model and the quantum standard WZW theory on elliptic curves and opens the way for the systematic use of the dynamical Hopf algebroids in the rational q-conformal field theory.
No associations
LandOfFree
Quasitriangular WZW model does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Quasitriangular WZW model, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Quasitriangular WZW model will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-565083