$w_{\infty}$-Currents in 3-Dimensional Toda Theory

TL;DR

This paper constructs and analyzes $w_{inite}$-currents in 3D Toda theory, deriving explicit spin 2 and 3 currents and verifying their algebraic consistency, advancing understanding of symmetries in integrable models.

Contribution

It introduces a novel $w_{inite}$-current framework for 3D Toda theory using Lax operators, providing explicit currents and confirming their algebraic structure.

Findings

Explicit spin 2 and 3 currents derived.

Poisson algebra of currents verified for consistency.

Framework enhances understanding of symmetries in 3D Toda theory.

Abstract

Chiral densities obeying a $w_{\infty}$ Poisson--bracket algebra are constructed for the $2+1\,\, A_{\infty}$ -- Toda field theory, using its alternative $w_{\infty}$ -- Toda representation. They are obtained from formal traces of powers of the Lax operator. The spin 2 and 3 currents are explicitely derived, and the consistency of their Poisson algebra is checked.