Bosonization and calculation of correlation functions in the Wess-Zumino-Witten model

D. Boyanovsky

Tigran Sedrakyan, Victor M. Galitski

Correlation functions in the Wess-Zumino-Novikov-Witten (WZNW) theory satisfy a system of Knizhnik-Zamolodchikov (KZ) equations, which involve constants of motion of an exactly solvable model, known as Gaudin magnet. We show that modified KZ equations, where the Gaudin operators are replaced by constants of motion of the closely related pairing Hamiltonian, give rise to a deformed WZNW model that contains terms breaking translational symmetry. This boundary WZNW model is identified and solved. The solution establishes a connection between the WZNW model and the pairing Hamiltonian in the theory of superconductivity. We also argue and demonstrate on an explicit example that our general approach can be used to derive exact solutions to a variety of dynamical systems.

J. F. van Diejen

Abstract It is known from work of Korff that the q -boson model with periodic boundary conditions gives rise to a q -deformation of the Wess–Zumino–Witten fusion algebra of type  . We employ recent results on the diagonalization of a finite aperiodic q -boson model with diagonal open end boundary conditions, so as to construct an analogous deformation of the Wess–Zumino–Witten fusion algebra of type B C ̂ .

N. M. Bogoliubov, Anatoli G. Izergin, N Kitanine

Alexei M. Tsvelik

In this paper, I revise arguments in favor of the PSL(2\ensuremath{\mid}2) Wess-Zumino-Novikov-Witten (WZNW) model as a theory of the plateau transition in integer quantum Hall effect. I show that all available numerical data (including the correlation length exponent $\ensuremath{\nu}$) are consistent with the predictions of such WZNW model with the level $k=8$.