Abstract
We revisit the classical theory of ten-dimensional two-derivative gravity coupled to fluxes, scalar fields, D-branes, anti D-branes and Orientifold-planes. We show that such set-ups do not give rise to a four-dimensional positive curvature spacetime with the isometries of de Sitter spacetime. We further argue that a de Sitter solution in type IIB theory may still be achieved if the higher-order curvature corrections are carefully controlled. Our analysis relies on the derivation of the de Sitter condition from an explicit background solution by going beyond the supergravity limit of type IIB theory. As such this also tells us how the background supersymmetry should be broken and under what conditions D-term uplifting can be realized with non self-dual fluxes.
Highlights
To suppression of higher-order terms in the Lagrangian by increasing powers of the cutoff, the predictions of inflation can be highly sensitive to corrections of both the potential or inflaton mass [11] and the kinetic terms [12, 13]
We further argue that a de Sitter solution in type IIB theory may still be achieved if the higher-order curvature corrections are carefully controlled
This ansatz is chosen as the M-theory uplift for the solution we want to obtain in Type IIB, i.e. by shrinking the torus specified by coordinates (z, z) or (x3, x11) to zero size one may recover type IIB theory
Summary
Consider the following Einstein-Hilbert action coupled to matter in D spacetime dimensions:. If the D-dimensional manifold has a direct product topology M4 × MD−4, the Ricci scalar for M4 is: R4 ≡ gμν Rμν. If R4 > 0 we obtain a positive curvature spacetime, of which de Sitter space is one example, as is consistent with our universe. (D − 6) Tμμ > 4Tmm. Whatever the content of the Lagrangian, we must satisfy (2.8) if we are to obtain a positively curved four-dimensional universe. We can still try to obtain an effective four-dimensional space at low energies. In this case, the transverse dimensions are not accessible, which is possible if the size of MD−4 is small compared to the typical distance scale of interactions in M4. We can proceed to analyse different choices for the Lagrangian
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