Duality in Quantum Toda theory and W-algebras

TL;DR

This paper explores duality properties in Quantum Toda theory linked to Lie algebras, revealing symmetries that interchange Dynkin diagrams and invert coupling constants, with specific examples for certain Lie types.

Contribution

It demonstrates a duality in conserved quantities of Quantum Toda theories, connecting conformal and affine cases, and provides explicit examples for specific Lie algebras.

Findings

Conserved quantities exhibit duality interchanging Dynkin diagrams and inverting coupling.

Duality relates conformal and affine Toda theories.

Explicit examples for B2, B3, and G2 Lie algebras are discussed.

Abstract

We consider Quantum Toda theory associated to a general Lie algebra. We prove that the conserved quantities in both conformal and affine Toda theories exhibit duality interchanging the Dynkin diagram and its dual, and inverting the coupling constant. As an example we discuss the conformal Toda theories based on $B_2,B_3$ and $G_2$ and the related affine theories.