Propagators on One-Loop Worldsheets for Orientifolds and Intersecting Branes

TL;DR

This paper derives one-loop propagators in superstring theory for complex backgrounds involving orbifolds, orientifolds, and intersecting D-branes, using a generalized method of images and dihedral groups.

Contribution

It introduces a generalized method of images to compute one-loop propagators with non-trivial holonomy and boundary conditions in superstring theory.

Findings

Derived explicit one-loop propagators for orbifold and orientifold backgrounds.

Extended the method of images to handle complex boundary conditions.

Highlighted the role of dihedral groups in constructing propagators.

Abstract

We obtain the one-loop propagators in superstring theory for the general case when the worldsheet fields satisfy non-trivial holonomy and/or boundary conditions. Non-trivial holonomy arises in orbifold and orientifold backgrounds whereas non-trivial boundary conditions arise in backgrounds containing D-branes of different dimensionality or D-branes intersecting each other at an angle. In our derivation, we use a generalized version of the method of images. Dihedral groups play a crucial role in constructing the one-loop propagators.