Smeared versus localised sources in flux compactifications

TL;DR

This work asks whether vacua found with smeared O$p$-planes or D$p$-branes in flux compactifications persist when the sources are localised. By analyzing Type II supergravity in 10D, the authors construct two BPS families linked to the GKP solution by T-duality, showing that localisation can preserve these smeared BPS structures via warp factors and flux redefinitions. They then show that a class of non-BPS AdS$_4$ solutions with smeared D3/anti-D3 sources does not survive localisation, casting doubt on the stringy consistency of smeared non-BPS vacua. The results illuminate when warping and flux backreaction cancel in the effective potential and underscore the special status of BPS configurations in enabling localisation, while highlighting potential instabilities for non-BPS constructions.

Abstract

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.

Figures (1)

• Figure 1: The smeared (left) versus localised (right) case.