Orientifolds and twisted boundary conditions

TL;DR

This paper explores the relationship between orientifold planes, T-duality, and twisted boundary conditions in gauge theories, providing methods to interpret D-brane configurations and reconstruct known results for classical groups on tori.

Contribution

It introduces a novel interpretation of crosscaps under T-duality as combinations of O+ and O- planes and develops a method to extract holonomies from D-brane positions in orientifold backgrounds.

Findings

T-dual of a crosscap is an O+ and O- plane combination

Holonomies can be read from D-brane positions in orientifolds

Reconstruction of gauge theory results on tori with twisted boundary conditions

Abstract

It is argued that the T-dual of a crosscap is a combination of an O+ and an O- orientifold plane. Various theories with crosscaps and D-branes are interpreted as gauge-theories on tori obeying twisted boundary conditions. Their duals live on orientifolds where the various orientifold planes are of different types. We derive how to read off the holonomies from the positions of D-branes in the orientifold background. As an application we reconstruct some results from a paper by Borel, Friedman and Morgan for gauge theories with classical groups, compactified on a 2-- or 3--torus with twisted boundary conditions.