A mechanism for addressing the “decompactification problem” is proposed, which consists of balancing the vacuum energy in Scherk-Schwarzed theories against contributions coming from non-perturbative physics. Universality of threshold corrections ensures that, in such situations, the stable minimum will have consistent gauge couplings for any gauge group that shares the same NN = 2 beta function for the bulk excitations as the gauge group that takes part in the minimisation. Scherk-Schwarz compactification from 6D to 4D in heterotic strings is discussed explicitly, together with two alternative possibilities for the non-perturbative physics, namely metastable SQCD vacua and a single gaugino condensate. In the former case, it is shown that modular symmetries gives various consistency checks, and allow one to follow soft-terms, playing a similar role to R-symmetry in global SQCD. The latter case is particularly attractive when there is nett Bose-Fermi degeneracy in the massless sector. In such cases, because the original Casimir energy is generated entirely by excited and/or non-physical string modes, it is completely immune to the non-perturbative IR physics. Such a separation between UV and IR contributions to the potential greatly simplifies the analysis of stabilisation, and is a general possibility that has not been considered before.
Abel, S. (2016). A dynamical mechanism for large volumes with consistent couplings. Journal of High Energy Physics, 2016(11), Article 085. https://doi.org/10.1007/jhep11%282016%29085