On the Partition Function for CP1-Instantons on a Flat Torus

Abstract

The partition function for the free theory of CP1-valued fields on a flat two-dimensional torus is studied. The partition function localizes to an infinite series of finite-dimensional integrals over the spaces of holomorphic and anti-holomorphic functions of fixed topological degree. The partition function measure on each of these spaces is computed explicitly, with respect to coordinates given by the zeroes and poles of the maps. Finally, the convergence properties of each of the integrals is discussed.