Fractional branes, warped compactifications and backreacted orientifold planes

TL;DR

This work shows that dynamical, worldvolume-dependent extensions of extremal $p$-brane solutions persist when fluxes corresponding to fractional branes are included, and it builds a precise map to warped compactifications via trading D$p$-branes for $O_p$-planes under RR tadpole constraints. The worldvolume dependence encoded in $H^W$ is interpreted as running scalars in the lower-dimensional no-scale potential, giving rise to supersymmetric or fake domain-wall flows in certain flux configurations, and providing explicit examples of backreacted orientifold planes with non-constant moduli. By constructing a smeared-to-localized transition, the paper clarifies when $H^W$ can be captured in lower-dimensional EFT and when full backreaction (the $H^T$ piece) must be accounted for, offering a concrete framework to test warped effective field theories in string compactifications. Overall, the results deepen the connection between higher-dimensional fractional-brane solutions and phenomenologically relevant warped backgrounds, with implications for moduli stabilization and supersymmetry in flux compactifications.

Abstract

The standard extremal p-brane solutions in supergravity are known to allow for a generalisation which consists of adding a linear dependence on the world-volume coordinates to the usual harmonic function. In this note we demonstrate that remarkably this generalisation goes through in exactly the same way for p-branes with fluxes added to it that correspond to fractional p-branes. We relate this to warped orientifold compactifications by trading the Dp-branes for Op-planes that solve the RR tadpole condition. This allows us to interpret the worldvolume dependence as due to lower-dimensional scalars that flow along the massless directions in the no-scale potential. Depending on the details of the fluxes these flows can be supersymmetric domain wall flows. Our solutions provide explicit examples of backreacted orientifold planes in compactifications with non-constant moduli.