Off-shell Crosscap State and Orientifold Planes with Background Dilatons

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 on-shell 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 RP2 worldsheet in the gauge in which the worldsheet curvature in the bulk of the fundamental region of the RP2 vanishes. We show that the non-trivial dilaton condensation reproduces the correct descent relation among orientifold plane tensions.