Integrable String Models in Terms of Chiral Invariants of SU(n), SO(n), SP(n) Groups

TL;DR

This paper develops new integrable string models using chiral invariants of SU(n), SO(n), and SP(n) groups, employing hydrodynamic methods and invariant currents to derive equations of hydrodynamic type, including nonlocal variants.

Contribution

It introduces novel integrable string equations based on chiral invariants and nonlocal currents, expanding the class of solvable models in string theory.

Findings

Constructed integrable string equations using chiral invariants of classical groups.

Developed hydrodynamic type equations on Riemannian spaces with and without torsion.

Formulated nonlocal string equations using Pohlmeyer tensor currents.

Abstract

We considered two types of string models: on the Riemmann space of string coordinates with null torsion and on the Riemman-Cartan space of string coordinates with constant torsion. We used the hydrodynamic approach of Dubrovin, Novikov to integrable systems and Dubrovin solutions of WDVV associativity equation to construct new integrable string equations of hydrodynamic type on the torsionless Riemmann space of chiral currents in first case. 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 in second case. We also used Pohlmeyer tensor nonlocal currents to construct new nonlocal string equation.