We investigate whether vacuum solutions in flux compactifications that are obtained with smeared sources (orientifolds or D-branes) still survive when the sources are localised. This seems to rely on whether the solutions are BPS or not. First we consider two sets of BPS solutions that both relate to the GKP solution through T-dualities: (p + 1)-dimensional solutions from spacetime-filling Op-planes with a conformally Ricci-flat internal space, and p-dimensional solutions with Op-planes that wrap a 1-cycle inside an everywhere negatively curved twisted torus. The relation between the solution with smeared orientifolds and the localised version is worked out in detail. We then demonstrate that a class of non-BPS AdS 4 solutions that exist for IASD fluxes and with smeared D3-branes (or analogously for ISD fluxes with anti-D3-branes) does not survive the localisation of the (anti) D3-branes. This casts doubts on the stringy consistency of non-BPS solutions that are obtained in the limit of smeared sources.

In this paper we investigate the localisation of SUSY-breaking branes which, in the smeared approximation, support specific non-BPS vacua. We show, for a wide class of boundary conditions, that there is no flux vacuum when the branes are described by a genuine delta-function. Even more, we find that the smeared solution is the unique solution with a regular brane profile. Our setup consists of a non-BPS AdS_7 solution in massive IIA supergravity with smeared anti-D6-branes and fluxes T-dual to ISD fluxes in IIB supergravity.Comment: 27 pages, Latex2e, 5 figure

We analyze infrared consistency conditions of 3D and 4D effective field theories with massive scalars or fermions charged under multiple U (1) gauge fields. At low energies, one can integrate out the massive particles and thus obtain a one-loop effective action for the gauge fields. In the regime where charge-independent contributions to higher-derivative terms in the action are sufficiently small, it is then possible to derive constraints on the charge-to-mass ratios of the massive particles from requiring that photons propagate causally and have an analytic S-matrix. We thus find that the theories need to contain bifundamentals and satisfy a version of the weak gravity conjecture known as the convex-hull condition. Demanding self-consistency of the constraints under Kaluza-Klein compactification, we furthermore show that, for scalars, they imply a stronger version of the weak gravity conjecture in which the charge-to-mass ratios of an infinite tower of particles are bounded from below. We find that the tower must again include bifundamentals but does not necessarily have to occupy a charge (sub-)lattice.

We improve on the understanding of the backreaction of anti-D6-branes in a flux background that is mutually BPS with D6-branes. This setup is analogous to the study of the backreaction of anti-D3-branes inserted in the KS throat, but does not require us to smear the anti-branes or do a perturbative analysis around the BPS background. We solve the full equations of motion near the anti-D6-branes and show that only two boundary conditions are consistent with the equations of motion. Upon invoking a topological argument we eliminate the boundary condition with regular H flux since it cannot lead to a solution that approaches the right kind of flux away from the anti-D6-branes. This leaves us with a boundary condition which has singular, but integrable, H flux energy density.

We show that the classical cosmological constant in type II flux compactifications can be written as a sum of terms from the action of localized sources plus a specific contribution from non-trivial background fluxes. Exploiting two global scaling symmetries of the classical supergravity action, we find that the flux contribution can in many interesting cases be set to zero such that the cosmological constant is fully determined by the boundary conditions of the fields in the near-source region. This generalizes and makes more explicit previous arguments in the literature. We then discuss the problem of putting D3-branes at the tip of the Klebanov-Strassler throat glued to a compact space in type IIB string theory so as to engineer a de Sitter solution. Our result for the cosmological constant and a simple global argument indicate that inserting a fully localized and backreacting D3-brane into such a background yields a singular energy density for the NSNS and RR 3-form field strengths at the D3-brane. This argument does not rely on partial smearing of the D3-brane or a linearization of field equations, but on a few general assumptions that we also discuss carefully.