On the Four-Dimensional Effective Action of Strongly Coupled Heterotic String Theory

TL;DR

This work derives the four-dimensional $N=1$ effective action from M theory on $S^1/Z_2$ with Witten's deformed Calabi–Yau background, identifying an expansion parameter $\epsilon\sim \kappa^{2/3}\rho/V^{2/3}$. The Kähler potential receives no $\kappa^{2/3}$ corrections when moduli are defined appropriately, while gauge-kinetic functions obtain $\kappa^{4/3}$ corrections and background fields generate $x^{11}$-dependent distortions that reproduce the weakly coupled one-loop structure in ten dimensions. At $\kappa^{4/3}$, a gauge-matter induced $|C|^2$ correction to the dilaton part of the Kähler potential and a corresponding threshold in the gauge couplings appear, with the real and imaginary parts arising from metric distortions and the CGG term, respectively. The results illustrate how strong coupling effects in heterotic M-theory can reproduce known weakly coupled results and reveal calculable, distortion-driven corrections guided by anomaly cancellation and Gauss–Bonnet boundary terms.

Abstract

The low-energy D=4, N=1 effective action of the strongly coupled heterotic string is explicitly computed by compactifying Horava-Witten theory on the deformed Calabi-Yau three-fold solution due to Witten. It is shown that, to order kappa^{2/3}, the Kahler potential is identical to that of the weakly coupled theory. Furthermore, the gauge kinetic functions are directly computed to order kappa^{4/3} and shown to receive a non-vanishing correction. Also, we compute gauge matter terms in the Kahler potential to the order kappa^{4/3} and find a nontrivial correction to the dilaton term. Part of those corrections arise from background fields that depend on the orbifold coordinate and are excited by four-dimensional gauge field source terms.