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تسجيل مستخدم جديدTowards an explicit construction of de Sitter solutions in classical supergravity
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Nakwoo Kim
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We revisit the stringy construction of four-dimensional de-Sitter solutions using orientifolds O$8_{pm}$, proposed by Cordova et al. arXiv:1911.04498. While the original analysis of the supergravity equations is largely numerical, we obtain semi-analytic solutions by treating the curvature as a perturbative parameter. At each order we verify that the (permissive) boundary conditions at the orientifolds are satisfied. To illustrate the advantage of our result, we calculate the four-dimensional Newton constant as a function of the cosmological constant. We also discuss how the discontinuities at O$8_-$ can be accounted for in terms of corrections to the worldvolume action.
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We find four-dimensional de Sitter compactifications of type IIA supergravity by directly solving the ten-dimensional equations of motion. In the simplest examples, the internal space has the topology of a circle times an Einstein manifold of negativ
e curvature. An orientifold acts on the circle with two fixed loci, at which an O8$_-$ and an O8$_+$ plane sit. These orientifold planes are fully backreacted and localized. While the solutions are numerical, the charge and tension of the orientifold planes can be verified analytically. Our solutions have moduli at tree level and can be made parametrically weakly-coupled and weakly-curved. Their fate in string theory depends on quantum corrections.
It was recently proposed that type IIA string theory may allow classical de Sitter solutions with O8-planes as the only localized sources. We show that such solutions are incompatible with the integrated supergravity equations of motion, analogously
to the no-go theorem due to Maldacena and Nu~{n}ez. We also discuss in detail divergences and discontinuities at the O8-plane positions and argue that they do not invalidate such an argument. We furthermore show that a recently proposed class of non-supersymmetric AdS solutions with O8-planes is in contrast with our results as well.
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e 4D potential arising from compactification on manfiolds with curvature, fluxes, and orientifold planes, we found that additional ingredients, beyond the minimal ones presented so far, are necessary to avoid the presence of unstable modes. We enumerate the minimal setups for (meta)stable de Sitter vacua to arise in this context.
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riginal solutions in more detail, focusing in particular on the O8$_-$ singularities and on the issues created by their boundary conditions. We also point out some previously known supersymmetric AdS solutions with the same local behavior at their O8$_-$ singularity.
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