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

Abstract

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.