  A supersymmetric theory in two-dimensions has enough data to define a
noncommutative space thus making it possible to use all the tools of
noncommutative geometry. In particular, we apply this to the N=1 supersymmetric
non-linear sigma model and derive an expression for the generalized loop space
Dirac operator, in presence of a general background, using canonical
quantization. The spectral action principle is used to show that the
superstring partition function is also a spectral action valid for the
fluctuations of the string modes.
