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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 …

) which are not observed (this is known as the moduli problem). … To stabilize the size and shape moduli one has to find ways to build a sufficiently complex potential for these moduli, which requires some extra ingredients (such as the ones existing in the KKLT construction …

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. …

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 …

Some of them have residual parameters - the moduli - and those are very interesting mathematically (and they are usually calculable, and often have some unbroken supersymmetry) but they are unacceptable … solutions only exist for the right values of the couplings that minimize the potential; the physical spectrum of "empty space" states is strictly vanishing away from the right stabilized value of the moduli …

Once they're there, they induce a superpotential that stabilizes some moduli, usually the complex structure moduli (the very "stabilizes" means that the allowed values of these moduli at which the total … The dilaton-axion field is stabilized by the Gukov-Vafa-Witten superpotential while nonperturbative effects are typically needed to stabilize the Kähler moduli. …

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

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. …

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 …

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 …

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? …

This question has many aspects because there are many groups of stringy vacua, some of them have been showed to have (unstabilized) moduli, the status of others was (or is) unknown. … In most classes of stringy vacua, the boundaries have been understood which means that it is known whether the vacua have some unstabilized moduli or not, and if they don't, the relevant potentials became …

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. …

This is the problem of radion stabilization for KK theories. The radion is the effective 4D field which measures the size of the compactified dimension. … For Calabi-Yau compactifications with unbroken SUSY, the radion turns out to be a moduli, which is experimentally unsatisfactory. …

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. …