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

TL;DR

This paper develops the classical and geometric description of open-string sectors in orientation orbifolds, including actions, branes, and Einstein equations, extending previous algebraic results to a broader class of models.

Contribution

It provides the classical WZW and sigma-model orientation-orbifold actions, branes, and Einstein equations, generalizing previous algebraic work to include classical and geometric aspects.

Findings

Derived the WZW orientation-orbifold action on the half cylinder.

Formulated the sigma-model orientation-orbifold action for a broad class of sectors.

Established the orientation-orbifold Einstein equations for 1-loop conformal sectors.

Abstract

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 {\it WZW orientation-orbifold action} -- which is naturally defined on the solid half cylinder -- and its associated WZW orientation-orbifold branes. As a generalization, we also obtain the {\it 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 {\it free boson} examples, the open-string WZW sectors above and the open-string sectors of the {\it general coset orientation orbifold}. Finally, we derive the {\it orientation- orbifold Einstein equations}, in terms of twisted Einstein tensors -- which hold when the twisted open-string sigma-model sectors are 1-loop conformal.