Spin Calogero-Moser periodic chains and two dimensional Yang-Mills theory with corners

Abstract

Quantum Calogero-Moser spin system is a superintegable system with the spectrum of commuting Hamiltonians that can be described entirely in terms of representation theory of corresponding simple Lie group. In this paper the underlying Lie group G is a compact connected, simply connected simple Lie group. It has a natural generalization known as quantum Calogero-Moser spin chain. In the first part of the paper we show that quantum Calogero-Moser spin chain is a quantum superintegrable systems. Then we show that the Euclidean multi-time propagator for this model can be written as a partition function of a two-dimensional Yang-Mills theory on a cylinder. Then we argue that the two-dimensional Yang-Mills theory with Wilson loops with "outer ends" should be regarded as the theory on space times with non-removable corners. Partition functions of such theory satisfy non-stationary Calogero-Moser equations.