The Fayet-Iliopoulos term in Type-I string theory and M-theory

The magnitude of the Fayet-Iliopoulos term is calculated for compactifications of Type-I string theory and Horava-Witten M-theory in which there exists a pseudo-anomalous U(1)X. Contrary to various conjectures, it is found that in leading order in the perturbative expansion around the weakly-coupled M-theory or Type-I limits, a result identical to that of the weakly-coupled E8×E8 heterotic string is obtained. The result is independent of the values chosen for the Type-I string scale or the size of the M-theory 11th dimension, only depending upon Newtonʹs constant and the unified gauge coupling.