Effective Orientifolds from Broken Supersymmetry

We recently proposed a class of type IIB vacua that yield, at low energies, four–dimensional Minkowski spaces with broken supersymmetry and a constant string coupling. They are compactifications with an internal five-torus bearing a five–form flux $\mathrm{\Phi }$ and warp factors depending on a single coordinate. The breaking of supersymmetry occurs when the internal space includes a finite interval. A probe-brane analysis revealed a gravitational repulsion and a charge attraction of equal magnitude from the left end of the interval, and a singularity at the other end. Here we complete the analysis revealing the presence, at one end, of an effective $O3$ of negative tension and positive five–form charge. We also determine the values of these quantities, and show that $T=-Q=\mathrm{\Phi }$, and characterize the singularity present at the other end of the interval, which hosts an opposite charge. Finally, we discuss various forms of the gravity action in the presence of a boundary and identify a self–adjoint form for its fluctuations.