Finding and solving Calogero-Moser type systems using Yang-Mills gauge theories

Abstract

Yang-Mills gauge theory models on a cylinder coupled to external matter charges provide powerful means to find and solve certain non-linear integrable systems. We show that, depending on the choice of gauge group and matter charges, such a Yang-Mills model is equivalent to trigonometric Calogero-Moser systems and certain known spin generalizations thereof. Choosing a more general ansatz for the matter charges allows us to obtain and solve novel integrable systems. The key property we use to prove integrability and to solve these systems is gauge invariance of the corresponding Yang-Mills model.

33 pages, no figures, to appear in Nucl. Phys. B

References in corpus (4)

• Generalized Calogero models through reductions by discrete symmetries
• Seiberg-Witten Theory and Integrable Systems
• Generalized Calogero-Sutherland systems from many-matrix models
• Novel integrable spin-particle models from gauge theories on a cylinder

Cited by in corpus (8)

• Novel Quantum States of the Rational Calogero Models Without the Confining Interaction
• Spin Calogero models obtained from dynamical r-matrices and geodesic motion
• On energy-critical half-wave maps into ${\mathbb{S}}^2$
• Goldfishing by gauge theory
• Global Well-Posedness For Half-Wave Maps With $S^2$ and ${\mathbb{H}}^2$ Targets For Small Smooth Initial Data
• Self-duality and scattering map for the hyperbolic van Diejen systems with two coupling parameters (with an appendix by S. Ruijsenaars)
• Canonical approach to the WZNW model
• Generalized spin Sutherland systems revisited