  We consider the holographic computation of two dimensional conformal field
theory partition functions on non-orientable surfaces. We classify the three
dimensional geometries that give bulk saddle point contributions to the
partition function, and find that there are fewer saddles than in the
orientable case. For example, for the Klein bottle there is a single smooth
saddle and a single additional saddle with an orbifold singularity. We argue
that one must generally include singular bulk saddle points in order to
reproduce the CFT results. We also discuss loop corrections to these partition
functions for the Klein bottle.
