Holography on Non-Orientable Surfaces

Understand

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.