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Integrable string models in terms of chiral invariants of \(SU(n), SO(n), SP(n)\) groups. (English) Zbl 1192.81267

Summary: We considered two types of string models: on the Riemann space of string coordinates with null torsion and on the Riemann-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 Riemann 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 Riemann 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.

MSC:

81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory
81T20 Quantum field theory on curved space or space-time backgrounds
81T40 Two-dimensional field theories, conformal field theories, etc. in quantum mechanics
81R12 Groups and algebras in quantum theory and relations with integrable systems
37J35 Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests
53Z05 Applications of differential geometry to physics
22E70 Applications of Lie groups to the sciences; explicit representations
81R05 Finite-dimensional groups and algebras motivated by physics and their representations
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