Ising model andN=2 supersymmetric theories

Abstract

We establish a direct link between massive Ising model and arbitrary massive N = 2 supersymmetric QFT's in two dimensions. This explains why the equations which appear in the computation of spin-correlations in the non-critical Ising model are the same as those describing the geometry of vacua in N = 2 theories. The tau-function appearing in the Ising model (i.e., the spin correlation function) is reinterpreted in the N = 2 context as a new ''index''. In special cases this new index is related to the Ray-Singer analytic torsion, and can be viewed as a generalization of that to the loop space of Kahler manifolds.