Abstract
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 N = 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. The large 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.
Highlights
The purpose of this paper is to argue that there is a way to realise order one couplings at large volume dynamically and without fine-tuning, providing a solution to the decompactification problem for a much broader class of models
It is argued that a general means of addressing the decompactification problem dynamically is to balance non-perturbative physics contributions to the vacuum energy against the Casimir energy in Scherk-Schwarzed theories
By contrast gauge symmetries with the wrong-sign beta function will remain as effectively global symmetries. Both the ISS mechanism and a single gaugino condensate were considered for the stabilising non-perturbative physics in the case of compactification from 6D to 4D in heterotic strings
Summary
It is convenient to proceed by developing the 5D example of the mechanism outlined in the Introduction, with the non-perturbative physics being the ISS mechanism. If one wishes to adopt the ISS results at face-value (with no extra KK modes to complicate things), one can impose a modest energy gap between the dynamical scale of the the SQCD theory and the mass-scale of the lowest lying KK modes, and in addition between the two sources of superymmetry breaking to ensure that the ISS analysis is not disrupted by the soft-terms that are already induced by the SS mechanism. The last constraint is on the elementary supersymmetric Dirac mass required in the ISS mechanism: it should take values mD 1/R It is simple and natural – not crucial – to take mD to be induced by the compactification, so that it too is proportional to 1/R, with constant of proportionality αD = RmD 1. It will be convenient to assume αD ∼ αF,B
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