Infinity Cancellation, Type I ′ Compactification and String S-matrix Functional

Nonvanishing tadpoles and possible infinities associated in the multiparticle amplitudes are discussed with regard to the disk and RP 2 diagrams of the Type I ′ compactification. We find that the infinity cancellation of SO(32) type I theory extends to this case as well despite the presence of tadpoles localized in the D-brane worldvolume and the orientifold surfaces. Formalism of string S-matrix generating functional is presented to find a consistent string background as c-number source function: we find this only treats the cancellation of the tadpoles in the linearized approximation. Our formalism automatically provides representation of the string amplitudes on this background to all orders in α. This work is supported in part by Grant-in-Aid for Scientific Research (07640403,08640372) and by the Grant-in-Aid for Scientific Research Fund (2126) from the Ministry of Education, Science and Culture, Japan. –1–