Novel integrable spin-particle models from gauge theories on a cylinder

Details Novel integrable spin-particle models from gauge theories on a cylinder Novel integrable spin-particle models from gauge theories on a cylinder

1998-04-08

arxiv.org/abs/solv-int/9804007v1

Phys. Lett. B, 429 (1998) 336-342

Physics

High Energy Physics

High Energy Physics - Theory

12 pages, LaTex

Scientific paper

10.1016/S0370-2693(98)00505-X

We find and solve a large class of integrable dynamical systems which includes Calogero-Sutherland models and various novel generalizations thereof. In general they describe $N$ interacting particles moving on a circle and coupled to an arbitrary number, $m$, of $su(N)$ spin degrees of freedom with interactions which depend on arbitrary real parameters $x_j$, $j=1,2,...,m$. We derive these models from SU(N) Yang-Mills gauge theory coupled to non-dynamic matter and on spacetime which is a cylinder. This relation to gauge theories is used to prove integrability, to construct conservation laws, and solve these models.

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