$SU(2,R)_q $ Symmetries of Non-Abelian Toda Theories

TL;DR

This paper investigates the classical and quantum symmetry structures of non-Abelian Toda models, revealing that a quantum deformed $SL(2,R)_q$ algebra governs their nonlocal currents and global charges.

Contribution

It demonstrates that the $SL(2,R)_q$ algebra forms the symmetry algebra of these models at both classical and quantum levels.

Findings

The $SL(2,R)_q$ Poisson brackets algebra is generated by chiral and antichiral charges.

This algebra includes nonlocal currents and a global U(1) charge.

The algebra appears as the symmetry algebra of the models.

Abstract

The classical and quantum algebras of a class of conformal NA-Toda models are studied. It is shown that the $SL(2,R)_q$ Poisson brackets algebra generated by certain chiral and antichiral charges of the nonlocal currents and the global U(1) charge appears as an algebra of the symmetries of these models.