Partition function for a nonlinear supersymmetric model

We analyse the nonlinear supersymmetric model associated with the Polyakov Euclidean sigma -model. In this theory the main point is to be able to comp ute the partition and correlation functions of interesting statistical vari ables, We briefly review some tools for renormalizing the partition functio n and we carry out the computations of the n-instanton contributions for a toy model on S-1; these are given explicitly in terms of specific hypergeom etric functions.