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We examine the vacuum structure of 4D effective theories of moduli fields in spacetime compactifications with quantized background fluxes. Imposing the no-scale structure for the volume deformations, we numerically investigate the distributions of flux vacua of the effective potential in complex structure moduli and axio-dilaton directions for two explicit examples in Type IIB string theory and F-theory compactifications. It turns out that distributions of non-supersymmetric flux vacua exhibit a non-increasing functional behavior of several on-shell quantities with respect to the string coupling. We point out that this phenomena can be deeply connected with a previously-reported possible correspondence between the flux vacua in moduli stabilization problem and the attractor mechanism in supergravity, and our explicit demonstration implies that such a correspondence generically exist even in the framework of F-theory. In particular, we confirm that the solutions of the effective potential we explicitly evaluated in Type IIB and F-theory flux compactifications indeed satisfy the generalized form of the attractor equations simultaneously.
In this work we analyze F-theory and Type IIB orientifold compactifications to study $alpha $-corrections to the four-dimensional, $mathcal{N} = 1$ effective actions. In particular, we obtain corrections to the Kahlermoduli space metric and its compl
In recent work, we conjectured that Calabi-Yau threefolds defined over $mathbb{Q}$ and admitting a supersymmetric flux compactification are modular, and associated to (the Tate twists of) weight-two cuspidal Hecke eigenforms. In this work, we will ad
We present the simplest model for classical transitions in flux vacua. A complex field with a spontaneously broken U(1) symmetry is embedded in $M_2times S_1$. We numerically construct different winding number vacua, the vortices interpolating betwee
We describe a method for finding flux vacua of type IIB string theory in which the Gukov-Vafa-Witten superpotential is exponentially small. We present an example with $W_0 approx 2 times 10^{-8}$ on an orientifold of a Calabi-Yau hypersurface with $(
These lectures provide a pedagogical, introductory review of the so-called Attractor Mechanism (AM) at work in two different 4-dimensional frameworks: extremal black holes in N=2 supergravity and N=1 flux compactifications. In the first case, AM dete