  The SO(32) heterotic superstring on a Calabi-Yau manifold can spontaneously
break supersymmetry at one-loop order even when it is unbroken at tree-level.
It is known that calculating the supersymmetry-breaking effects in this model
gives a relatively accessible test case of the subtleties of superstring
perturbation theory in the RNS formalism. In the present paper, we calculate
the relevant amplitudes in the pure spinor approach to superstring perturbation
theory, and show that the regulator used in computing loop amplitudes in the
pure spinor formalism leads to subtleties somewhat analogous to the more
familiar subtleties of the RNS approach.
