The Spectral Problem for the q-Knizhnik-Zamolodchikov Equation
Peter G. O. Freund, Anton V. Zabrodin
TL;DR
This paper investigates the spectral problem of the q-Knizhnik-Zamolodchikov equations for quantum affine algebra U_q(sl_2) at level zero, providing explicit solutions and connecting the S-matrix to the XXZ antiferromagnet.
Contribution
It offers a detailed analysis of 2-point functions, explicitly constructs scattering states using q-Jacobi polynomials, and links the S-matrix to the XXZ model's kink-antikink scattering.
Findings
Explicit solutions for scattering states in terms of q-Jacobi polynomials
Identification of the S-matrix with the kink-antikink S-matrix in XXZ antiferromagnet
Analysis of the spectral problem at level zero for U_q(sl_2)
Abstract
We analyse the spectral problem for the q-Knizhnik-Zamolodchikov equations for at level zero. The case of 2-point functions in the fundamental representation is studied in detail. The scattering states are found explicitly in terms of continuous q-Jacobi polynomials. The corresponding S-matrix is shown to coincide, up to a trivial factor, with the kink-antikink S-matrix in the spin-1/2 XXZ antiferromagnet.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.