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 Φ 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, together with 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, showing that T = −Q = Φ, 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.