My research projects:
Alexei Morozov, Hasib Sifat, Itzykson-Zuber correlators from character expansion, Eur. Phys. J. C 85, (2025) 648. DOI: 10.1140/epjc/s10052-025-14374-9; arXiv: 2504.05292
Abstract: We demonstrate the consistency of character expansion for the Itzykson-Zuber (IZ) model in terms of Schur polynomials with the old formulas for pair correlators with the IZ measure. An essential new feature of the correlators is that they are not symmetric in eigenvalues – and thus can not be expressed through Schur polynomials only. Instead, we demonstrate that an expression is possible in terms of Schur derivatives. This opens a new way to study arbitrary IZ correlators of any order in character expansion.
Alexei Morozov, Hasib Sifat, Conformal blocks of Wess-Zumino-Witten model from its free-field representation (arXiv: 2511.23132) [Submitted to the Journal of High Energy Physics (JHEP)]
A powerful approach to the celebrated Wess-Zumino-Witten (WZW) model is provided by its free-field realization. However, explicit calculations of conformal blocks are not described in the literature in full detail. We begin this study with the simplest cases of the $\hat{sl}(2)_k$ and $\hat{sl}(3)_k$ WZW models, with special emphasis on their global $sl(2)$ and $sl(3)$ symmetries of the resulting correlators, which are not explicit in this formalism. Also non-trivial is the verification of the Knizhnik-Zamolodchikov equations in the $\hat{sl}(3)_k$ case, where the answers take the form of double integrals over screening charge positions and do not look like ordinary hypergeometric functions.