Holography on Non-Orientable Surfaces

TL;DR

This paper studies the holographic duals of 2D conformal field theories on non-orientable surfaces, classifies bulk geometries, and emphasizes the importance of including singular saddle points for accurate results.

Contribution

It classifies bulk geometries for holographic CFTs on non-orientable surfaces and highlights the necessity of considering singular saddles to match CFT computations.

Findings

Fewer bulk saddles exist for non-orientable surfaces compared to orientable ones.

A single smooth and a singular saddle contribute to the Klein bottle partition function.

Loop corrections are discussed for the Klein bottle case.

Abstract

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.