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

TL;DR

The paper shows that in leading order, the Fayet-Iliopoulos term for a pseudo-anomalous U(1)$_X$ in Type-I string theory and Horava-Witten M-theory reproduces the same magnitude as in the weakly-coupled E$_8\times$E$_8$ heterotic string, namely $\xi^2 = {A g_{\rm unif}^2 M_*^2 \over 192\pi^2}$, independent of the Type-I scale or the 11th-dimension length. The result is obtained by linking the anomaly coefficient to the model-independent axion, computing the axion kinetic normalization $N$ from dimensional reduction in HW/M-theory and Type-I theories, and expressing the FI term in terms of $G_N$ and $\alpha_{\rm unif}$. This indicates a robustness of the FI-term prediction across strong-coupling limits, with implications for SUSY breaking mediation and inflation scenarios, while noting caveats if MSSM gauge sectors arise from D-brane dynamics. The analysis relies on the Green-Schwarz mechanism, the coupling of the dilaton/axion, and the relation between four-dimensional couplings and higher-dimensional parameters.

Abstract

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 E_8xE_8 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 Newton's constant and the unified gauge coupling.