  A supersymmetric theory in two-dimensions has enough data to define a
noncommutative space thus making it possible to use all 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 then used to determine a spectral action valid
for the fluctuations of the string modes.
