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Register a new userF-theory Vacua and $alpha$-Corrections
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Authors
Matthias Weissenbacher
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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 complex structure for generic dimension originating from eight-derivative corrections to eleven-dimensional supergravity. We propose a completion of the $G^ 2 R^3$ and $( abla G)^2R^2$-sector in eleven-dimensions relevant in Calabi--Yau fourfold reductions. We suggest that the three-dimensional, $mathcal{N}=2$ Kahler coordinates may be expressed as topological integrals depending on the first, second, and third Chern-forms of the divisors of the internal Calabi--Yau fourfold. The divisor integral Ansatz for the Kahler potential and Kahler coordinates may be lifted to four-dimensional, $mathcal{N} = 1$ F-theory vacua. We identify a novel correction to the Kahler potential and coordinates at order $ alpha^2$, which is leading compared to other known corrections in the literature. At weak string coupling the correction arises from the intersection of $D7$-branes and $O7$-planes with base divisors and the volume of self-intersection curves of divisors in the base. In the presence of the conjectured novel $alpha$-correction resulting from the divisor interpretation the no-scale structure may be broken. Furthermore, we propose a model independent scenario to achieve non-supersymmetric AdS vacua for Calabi-Yau orientifold backgrounds with negative Euler-characteristic.
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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.
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The Schwarzschild, Schwarzschild-AdS, and Schwarzschild-de Sitter solutions all admit freely acting discrete involutions which commute with the continuous symmetries of the spacetimes. Intuitively, these involutions correspond to the antipodal map of the corresponding spacetimes. In analogy with the ordinary de Sitter example, this allows us to construct new vacua by performing a Mottola-Allen transform on the modes associated with the Hartle-Hawking, or Euclidean, vacuum. These vacua are the `alpha-vacua for these black holes. The causal structure of a typical black hole may ameliorate certain difficulties which are encountered in the case of de Sitter alpha-vacua. For Schwarzschild-AdS black holes, a Bogoliubov transformation which mixes operators of the two boundary CFTs provides a construction of the dual CFT alpha-states. Finally, we analyze the thermal properties of these vacua.
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