Fractional branes, warped compactifications and backreacted orientifold planes

Understand

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.