Abstract
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 worldvolume 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.
Highlights
Which sources are smeared) at least captures the correct on-shell value for the moduli and the cosmological constant
One method to develop or test WEFT proposals is to construct fully backreacted tendimensional solutions and dimensionally reduce them to check the consistency of the lower-dimensional WEFT. This strategy has been followed in [5, 6, 15, 18, 20, 22]. It is the aim of this paper to continue with this strategy and take a first step towards constructing general non-trivial backreacted solutions that do not describe critical points of the lowerdimensional theory but dynamical solutions with non-constant scalars
In this paper we focus on the solutions and their interpretation in the WEFT, but the actual application to constructing and testing WEFT will be done elsewhere
Summary
P+1 and the coordinates along the transversal space are yi with i = 1, . Where ⋆9−p is with respect to the transversal space metric ds29−p.3 Both the worldvolume metric and transversal metric are taken to be Ricci flat: ds2p+1 = gaWb dxadxb , ds29−p = giTj dyidyj , Rab(gW ) = 0 , Rij(gT ) = 0. The most well known solutions are those corresponding to string theory Dp-branes in flat space, for p = 0, . GW is the Minkowski metric, gT the metric on flat Euclidean space and the harmonic functions are HW = 0, HT (r). Where r is the radial coordinate in the transversal space. For a flat worldvolume the solution for HW is most written in Cartesian coordinates. Since x0 is the time-direction we can for instance make timedependent brane solutions in this way [25]
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