On the Target-Space Geometry of Open-String Orientation-Orbifold Sectors

Including world-sheet orientation-reversing automorphisms in the orbifold program, we recently reported the twisted operator algebra and twisted KZ equations in each open-string sector of the general WZW orientation orbifold. In this paper we work out the corresponding classical description of these sectors, including the WZW orientation-orbifold action – which is naturally defined on the solid half cylinder – and its associated WZW orientationorbifold branes. As a generalization, we also obtain the sigma-model orientation-orbifold action, which describes a much larger class of open-string orientation-orbifold sectors. As special cases, this class includes twisted open-string free boson examples, the open-string WZW sectors above and the open-string sectors of the general coset orientation orbifold. Finally, we derive the orientation-orbifold Einstein equations, in terms of twisted Einstein tensors – which hold when the twisted open-string sigma model sectors are 1-loop conformal.