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We argue that the problem of finding lower-dimensional de Sitter solutions to the classical field equations of higher-dimensional supergravity necessarily requires understanding the back-reaction of whatever localized objects source the bulk fields.
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S. M. Carroll and M. M. Guica, “Sidestepping the cosmological constant with football-shaped extra dimensions,” arXiv:hep-th/0302067; Y. Aghababaie, C. P. Burgess, S. L. Parameswaran, F. Quevedo, “SUSY breaking and moduli stabilization from fluxes in gauged 6-D supergravity,” JHEP 0303
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E. Silverstein, “Simple de Sitter Solutions,” Phys. Rev. D77
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