Off - shell Crosscap State and Orientifold Planes

We show that a non-trivial dilaton condensation alters the dimensions of orientifold planes. An off-shell crosscap state which naturally interpolates between the usual onshell crosscap states and their T-duals plays an important role in the analysis. We present an explicit representation of the off-shell crosscap state on an RP 2 worldsheet in the gauge in which the worldsheet curvature in the bulk of the fundamental region of the RP 2 vanishes. We show that the non-trivial dilaton condensation reproduces the correct descent relation among orientifold plane tensions. This work is supported in part by the Grant-in-Aid for Scientific Research (14540264) from the Ministry of Education, Science and Culture, Japan. e-mail: [email protected] e-mail: [email protected]