Smeared versus localised sources in flux compactifications

TL;DR

This paper examines the validity of flux compactification solutions with smeared sources when sources are localized, revealing that non-BPS solutions with smeared sources often do not survive localization, questioning their string theory consistency.

Contribution

It provides a detailed analysis of the impact of source localization on flux compactification solutions, especially distinguishing between BPS and non-BPS cases.

Findings

BPS solutions related by T-duality are consistent upon localization.

Non-BPS AdS_4 solutions with smeared D3-branes do not survive localization.

Smeared non-BPS solutions may lack stringy consistency.

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.