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Localised sources such as D-branes or orientifold planes play an importantrole in many string compactifications that are relevant for phenomenology. Thepresence of these objects typically induces complicated dynamics in the compactdimensions such that a full solution to the 10d equations of motion is oftenout of reach. In order to still be able to make statements about the 4deffective theory arising in the low-energy limit, the equations of motion areusually only solved in an integrated sense, while the backreaction of thelocalised sources on the internal fields is neglected. This simplification isoften referred to as smearing. In this work, we investigate to what extentsmearing may affect observables in the effective low-energy theory and whetherit may lead to fake solutions that would cease to exist once the backreactionis properly taken into account. We analyse explicit examples for which smearedsolutions exist and find that the reliability of the smeared approximationappears to depend on whether or not these solutions saturate a BPS bound. Wealso address the proposal of placing anti-D3-branes at the tip of a warpedthroat geometry like the Klebanov-Strassler solution in order to constructmeta-stable de Sitter vacua in string theory. We show that, under a few generalassumptions, the backreaction of the fully localised anti-branes yields asingularity in fields that do not directly couple to them, and we give anargument suggesting that the singularity is not resolved by brane polarisation.We furthermore demonstrate that, in many string compactifications involvingnon-trivial background fluxes, the effective lower-dimensional cosmologicalconstant is determined by the on-shell action of the localised sources presentin the solution. This often allows to compute the cosmological constant withoutresorting to potentially unreliable approximations like smearing.

Backreaction of Localised Sources in String Compactifications