The Integrals of Motion for the Deformed W-Algebra Wqt(sl_N^)

TL;DR

This paper reviews the deformed W-algebra Wqt(sl_N^), constructs its local and nonlocal integrals of motion explicitly, and demonstrates their commutation properties, extending known results to an elliptic setting.

Contribution

It provides explicit constructions of integrals of motion for the deformed W-algebra Wqt(sl_N^), including their elliptic generalizations, which were not previously detailed.

Findings

Integrals of motion commute with each other.

Explicit formulas for local and nonlocal integrals of motion.

Extension of elliptic versions of integrals for Virasoro and W(sl_3^) algebras.

Abstract

We review the deformed W-algebra Wqt(sl_N^) and its screening currents. We explicitly construct the local integrals of motion I_n for this deformed W-algebra. We explicitly construct the nonlocal integrals of motion G_n by means of the screening currents. Our integrals of motion commute with each other, and give the elliptic version of those for the Virasoro algebra and the W-algebra W(sl_3^), obtained by V.Bazhanov, A.Hibberd, S.Khoroshkin, S.Lukyanov and Al.Zamolodchikov.