A $\hbar$-deformation of the $W_{N}$ algebra and its vertex operators

TL;DR

This paper introduces a novel $$-deformation of the $W_{N}$ algebra, deriving its quantum Miura transformation, vertex operators, and commutation relations, advancing the understanding of deformed algebraic structures.

Contribution

It presents the first explicit construction of an $$-deformation of the $W_{N}$ algebra along with its vertex operators and quantum Miura transformation.

Findings

Derived the $$-deformed $W_{N}$ algebra

Constructed vertex operators for the deformed algebra

Established commutation relations for the deformed algebra

Abstract

In this paper,we derive a $\hbar$-deformation of the $W_{N}$ algebra and its quantum Miura tranformation. The vertex operators for this $\hbar$-deformed $W_{N}$ algebra and its commutation relations are also obtained.