We set up a general lattice version of non-linear σ models defined on homogeneous spaces. We then apply this to the CPn-1 models which are the correct extension of the SU(2) σ model to SU(N). We exhibit their "confinement" property: the elementary multiplets Zα used to describe the system do not appear as physical particles but only as bound states ZαλαβaZβ. The method enable us to examine the "θ vacua" in the strong coupling limit by using a "dilute loop" approximation. We discuss the effect of the low activation energy for instantons which means that on a lattice, topological number is not conserved.
ASJC Scopus subject areas
- Nuclear and High Energy Physics