de Sitter Vacua from Ten Dimensions

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}.
Comment: 58 pages. v2: corrected statements about generalized complex geometry. Appendices contain more details of spinor ansatz and of D3-brane potential. Typos fixed, refs added. v3: significant additional results. Appendix A includes analysis of a new term in the Killing spinor equations. Appendix C contains a demonstration of the cancellation of divergences. Conclusions unchanged