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In order to violate this bound on the number of gauge generators, you need a lot of branes in some kind of type II theory, and then you won't be able to stabilize the compactification at a small enough … When the low-energy theory is supersymmetric, it often has parameters, and moduli, which you can vary while keeping the theory supersymmetric. …

As for the instability of string compactifications, this is actually a long-standing topic in string theory, in areas like "moduli stabilization" and the possible instability of De Sitter space and Anti … The size and shape of the extra dimensions and other geometric parameters, are known as "moduli", and there are models in which the dark matter comes from excitations of the moduli. …

The only serious study I'm aware of, of moduli stabilization on such manifolds, is this 2007 paper, part of a series of papers developing the "G2-MSSM", a paradigm for obtaining the MSSM from such compactifications …

Examples for models with such moduli stabilization are the KKLT mechanism ("de Sitter Vacua in String Theory" by Kachru, Kallosh, Linde, Trivedi) or Randall-Sundrum models (a non-string-theoretic example … This is very much not an exhaustive list, but the "mechanism" for moduli stabilization will differ in each individual case - the only overall property shared is that there will be some moduli fields that …

The latter identitication is useful because it gives an straightforward way to construct and compute the dimension of the the scalar and vector moduli spaces as 28 scalars of the form $G_{nm}$ and other … Not to mention the need of a moduli stabilization mechanism. …

My guess would be that it isn't, since the possible stabilized vacua form a discrete set, and the moduli should vary continuously. … Why is it unavoidable that the moduli of the Calabi-Yau manifold are dynamic? Couldn't it be that the Calabi-Yau manifold with all its structure (metric, complex) is fixed as a model parameter? …

Just as a technical point, continuously varying the moduli of one Calabi-Yau can end up with another Calabi-Yau; this is an aspect of mirror symmetry. … Moduli can be rigid. But it is the exception rather than the rule. …

So-called "moduli stabilization" is a major area of research. The dilaton mass and dilaton vev in string theory are examples of this problem. For unbroken supersymmetry, the dilaton mass is zero. … You can find further papers by looking for "dilaton stabilization". …

are more constraints on such a model than are usually imposed on model building in particle physics alone: the model is not only supposed to reproduce the fundamental particle content but also address moduli … stabilization, the cosmological constant and dark matter. …

The problem of "stabilizing" these moduli, hence to make the model be such that these moduli fields have mass outside the range of existing accelerator experiments, has been the huge topic in string theory … the way to a point as a classical manifold, so that only a classically 0-dimensional space but non-classically (non-commutative) still with "KO-dimension" 6 remains, then also its spurious Riemannian moduli …

Since these so-called moduli degrees of freedom are usually unstable, a realistic theory must incorporate some mechanism of moduli-stabilization. …

The technical name is the problem of "moduli stabilization" in string theory, because there some fields (called moduli) the values of which determine the size of the dimensions. … There have been many attempts to stabilize the moduli in different string constructions, ie to find a way to predict the size of all dimensions in nature without putting them in by hand, but I think it …

I'd like to do the maths for the moduli stabilization of 6D Einstein-Maxwell Gravity $$ S= \int d^6X \sqrt{-G_6}(M_6^4R_6[G_6]-M_6^2|F_2|^2), $$ where the 6D metric is specified by $$ ds^2 = g_{\mu\nu …

Quite generally, too simple or too supersymmetric vacua tend to have some exact moduli but the most generic SUSY-breaking stationary point has no moduli left. …

So they're zero-dimensional classes with no moduli left. … So there are no moduli left. We say that they are stabilized vacua. …