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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 …

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. …

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 …

Type IIB on a CY orientifold $X$, one uses fluxes to stabilize the axio-dilaton $\tau$ and the complex structure moduli $z_a$ - the periods of the holomorphic three-form $\Omega$ over the basis three-cycles … However, once we include the non-perturbative corrections to $W$ to stabilize the Kahler moduli and break supersymmetry by e.g. an anti-D3 brane, the scalar potential is no longer positive-definite. …

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 …

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". …

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 …

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? …

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. …

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. …

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 …

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

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. …

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. …