Classifying orientifolds by flat n-gerbes

TL;DR

This paper classifies supersymmetric orientifold configurations on toroidal orbifolds by analyzing flat n-gerbes associated with orientifold planes, linking geometric charges to string compactification consistency.

Contribution

It introduces a classification method for orientifold configurations using flat n-gerbes, extending understanding of their charges and duality properties in string theory.

Findings

Classification of all supersymmetric orientifolds on T^k/Z_2 for k ≤ 6.

Identification of SL(2,Z) orbits in the k=6 case.

Expressions for local gerbe-holonomies around orientifold planes.

Abstract

The discrete tensorial charges carried by orientifold planes define n-gerbes in space-time. The simplest way to ensure a consistent string compactification is to require these gerbes to be flat. This results in expressions for the local gerbe-holonomies around each orientifold plane, describing its charges. Inverting the procedure and considering all flat gerbes leads to a classification of orientifold configurations. Requiring that the tadpole is cancelled by adding D-branes, we classify all supersymmetric orientifolds on T^k/Z_2 with 2^k O(9-k) planes at the fixed points, for k less or equal to 6. For k=6 these theories organize in orbits of the SL(2,Z) S-duality symmetry of N=4 supersymmetric gauge theories.