Non-perturbative Resolution of Strong Coupling Singularities in 4d N=1 Heterotic/M-theory

We investigate the interior of the moduli space of four-dimensional $\mathcal{N}=1$ theories of gravity arising from compactifications of the $E_8\times E_8$ heterotic string on Calabi-Yau threefolds. By studying the threshold corrections to the coupling of the heterotic gauge groups, we infer the existence of a strong coupling singularity for one of the perturbative heterotic gauge groups, which effectively yields an additional finite distance boundary of the classical scalar field space. In heterotic M-theory, this boundary maps to a domain wall solution for which the gauge coupling and the warp factor on one of the Horava-Witten 9-branes diverge, thus highlighting the gravitational origin of the classical strong coupling singularity. The divergence of the warp factor is, however, regulated once non-perturbative effects are taken into account, as we demonstrate by studying the instanton corrections to the 5d BPS domain wall equations. This regularization implies that the classical strong coupling boundary of the scalar field 4d $\mathcal{N}=1$ heterotic/M-theory is resolved, indicating that, at the quantum level, the field space can be extended beyond this classical boundary.