  The gaugino propagator is calculated by explicitly considering the
propagation of a heterotic string between two different points in space-time
using the non-trivial world-sheet conformal field theory for the fivebrane
background. We find that there are no propagations of gaugino which is in the
spinor representation of the non-trivial four-dimensional space of the
fivebrane background. This result is consistent with the arguments on the
fermion zero-modes of the fivebrane background in the low-energy heterotic
supergravity theory. Furthermore, assuming the continuous limit to the flat
space-time background at the place far away from the fivebrane, we suggest an
effective propagator which is effective only at the place far away from the
fivebrane in the flat space-time limit. From the effective propagator we
evaluate a possible gaugino pair condensation. The result is consistent with
the suggested scenario of the gaugino condensation in the fivebrane background
in the low-energy heterotic supergravity theory.
