How flux compactification solves the moduli space problem in string theory? Please provide some details and, if posible, an example.
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1$\begingroup$ yeah, i would like to know about this too, specifically what role does it do in the whole stabilization (some would say freezing) business $\endgroup$– lurscherCommented Jun 28, 2011 at 14:39
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Nonzero fluxes are required because of some equations of motion linking them to a nonzero Euler character. 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 potential has a local minimum is discrete, assuming fixed values of other moduli).
The dilaton-axion field is stabilized by the Gukov-Vafa-Witten superpotential while nonperturbative effects are typically needed to stabilize the Kähler moduli.
See
http://motls.blogspot.com/2006/04/flux-compactifications-of-m-theory-and.html
This is of course a big technical topic and the literature on stabilized flux vacua is large. One can't describe everything in a single comment. The Becker-Becker-Schwarz textbook probably has a good treatment of these matters.
answered Jun 28, 2011 at 18:27