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Register a new userSingle-step de Sitter vacua from non-perturbative effects with matter
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A scenario of moduli stabilisation based on the interplay between closed and open string sectors is explored in a bottom-up approach. We study N=1 effective supergravities inspired by type IIB orientifold constructions that include background fluxes and non-perturbative effects. The former generate the standard flux superpotential for the axiodilaton and complex structure moduli. The latter can be induced by gaugino condensation in a non-Abelian sector of D7-branes and involve the overall Kaehler modulus of the compactification as well as matter fields. We analyse the dynamics of this coupled system and show that it is compatible with single-step moduli stabilisation in a metastable de Sitter vacuum. A novelty of the scenario is that the F-term potential suffices to generate a positive cosmological constant and to stabilise all moduli, except for a flat direction that can be either lifted by a mass term or eaten up by an anomalous U(1).
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The properties of the effective scalar potential are studied in the framework of type IIB string theory, taking into account perturbative and non-perturbative corrections. The former modify the Kahler potential and include $alpha$ and logarithmic corrections generated when intersecting D7 branes are part of the internal geometric configuration. The latter add exponentially suppressed Kahler moduli dependent terms to the fluxed superpotential. The possibility of partial elimination of such terms which may happen for particular choices of world fluxes is also taken into account. That being the case, a simple set up of three Kahler moduli is considered in the large volume regime, where only one of them is assumed to induce non-perturbative corrections. It is found that the shape of the F-term potential crucially depends on the parametric space associated with the perturbative sector and the volume modulus. De Sitter vacua can be obtained by implementing one of the standard mechanisms, i.e., either relying on D-terms related to $U(1)$ symmetries associated with the $D7$ branes, or introducing $overline{D3}$ branes. In general it is observed that the combined effects of non-perturbative dynamics and the recently introduced logarithmic corrections lead to an effective scalar potential displaying interesting cosmological and phenomenological properties.
We analyze the de Sitter construction of cite{KKLT} using ten-dimensional supergravity, finding exact agreement with the four-dimensional effective theory. Starting from the fermionic couplings in the D7-brane action, we derive the ten-dimensional stress-energy due to gaugino condensation on D7-branes. We demonstrate that upon including this stress-energy, as well as that due to anti-D3-branes, the ten-dimensional equations of motion require the four-dimensional curvature to take precisely the value determined by the four-dimensional effective theory of cite{KKLT}.
We study the arguments given in [1] which suggest that the uplifting procedure in the KKLT construction is not valid. First we show that the modification of the SUSY breaking sector of the nilpotent superfield, as proposed in [1], is not consistent with non-linearly realized local supersymmetry of de Sitter supergravity. Keeping this issue aside, we also show that the corresponding bosonic potential does actually describe de Sitter uplifting.
We propose a new mechanism for obtaining de Sitter vacua in type IIB string theory compactified on (orientifolded) Calabi-Yau manifolds similar to those recently studied by Kachru, Kallosh, Linde and Trivedi (KKLT). dS vacuum appears in KKLT model after uplifting an AdS vacuum by adding an anti-D3-brane, which explicitly breaks supersymmetry. We accomplish the same goal by adding fluxes of gauge fields within the D7-branes, which induce a D-term potential in the effective 4D action. In this way we obtain dS space as a spontaneously broken vacuum from a purely supersymmetric 4D action. We argue that our approach can be directly extended to heterotic string vacua, with the dilaton potential obtained from a combination of gaugino condensation and the D-terms generated by anomalous U(1) gauge groups.
We develop a method for constructing metastable de Sitter vacua in N=1 supergravity models describing the no-scale volume moduli sector of Calabi-Yau string compactifications. We consider both heterotic and orientifold models. Our main guideline is the necessary condition for the existence of metastable vacua coming from the Goldstino multiplet, which constrains the allowed scalar geometries and supersymmetry-breaking directions. In the simplest non-trivial case where the volume is controlled by two moduli, this condition simplifies and turns out to be fully characterised by the intersection numbers of the Calabi-Yau manifold. We analyse this case in detail and show that once the metastability condition is satisfied it is possible to reconstruct in a systematic way the local form of the superpotential that is needed to stabilise all the fields. We apply then this procedure to construct some examples of models where the superpotential takes a realistic form allowed by flux backgrounds and gaugino condensation effects, for which a viable vacuum arises without the need of invoking corrections to the Kahler potential breaking the no-scale property or uplifting terms. We finally discuss the prospects of constructing potentially realistic models along these lines.
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