Orientifolds and twisted boundary conditions Original Research Article

It is argued that the T-dual of a cross-cap is a combination of an O+ and an O− orientifold plane. Various theories with cross-caps 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.