Deformations of W-algebras associated to simple Lie algebras

TL;DR

This paper introduces deformed W-algebras linked to simple Lie algebras, providing explicit formulas and revealing connections to integrable models and affine Toda theories.

Contribution

It defines the deformed W-algebra _{q,t}() for any simple Lie algebra, including free field realizations, screening operators, and explicit generators for classical types.

Findings

Explicit formulas for generators of _{q,t}() for classical Lie algebras

Connection between _{q,t}() and analytic Bethe Ansatz in integrable models

Scaling limit relates to affine Toda field theories

Abstract

Deformed $\W$--algebra $\W_{q,t}(\g)$ associated to an arbitrary simple Lie algebra $\g$ is defined together with its free field realizations and the screening operators. Explicit formulas are given for generators of $\W_{q,t}(\g)$ when $\g$ is of classical type. These formulas exhibit a deep connection between $\W_{q,t}(\g)$ and the analytic Bethe Ansatz in integrable models associated to quantum affine algebras $U_q(\G)$ and $U_t(\GL)$. The scaling limit of $\W_{q,t}(\g)$ is closely related to affine Toda field theories.