Integrable string models with constant torsion in terms of chiral invariants of SU(n), SO(n), SP(n) groups

TL;DR

This paper constructs new integrable string equations of hydrodynamic type using invariant local chiral currents of principal chiral models for SU(n), SO(n), and SP(n) groups, expanding the understanding of integrable systems with constant torsion.

Contribution

It introduces a novel method to formulate integrable string equations based on chiral invariants and Casimir operators for multiple Lie groups.

Findings

Derived new integrable string equations of hydrodynamic type

Utilized invariant local chiral currents for SU(n), SO(n), SP(n)

Connected chiral invariants to Hamiltonian formulations

Abstract

We used the invariant local chiral currents of principal chiral models for SU(n), SO(n), SP(n) groups to construct new integrable string equations of hydrodynamic type on the Riemmann space of the chiral primitive invariant currents and on the chiral non-primitive Casimir operators as Hamiltonians.