Infinity Cancellation, Type I' Compactification and String S-Matrix Functional

TL;DR

This paper explores tadpole cancellations and infinities in Type I' string compactifications, introducing a string S-matrix formalism that ensures consistent backgrounds and amplitude representations to all orders in alpha'.

Contribution

It extends infinity cancellation results to Type I' compactifications with localized tadpoles using a novel S-matrix generating functional formalism.

Findings

Infinities cancel in Type I' despite localized tadpoles.

The S-matrix formalism provides all-order amplitude representations.

Tadpole cancellation is achieved in the linearized approximation.

Abstract

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 world-volume 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 $\alpha'$.