Loop effects in pseudosupersymmetry

We analyze the transmission of supersymmetry breaking in brane-world models of pseudosupersymmetry. In these models two branes preserve different halves of the bulk supersymmetry. Thus supersymmetry is broken although each sector of the model is supersymmetric when considered separately. The world-volume theory on one brane feels the breakdown of supersymmetry only through two-loop interactions involving a coupling to fields from the other brane. In a 5D toy model with bulk vectors, we compute the diagrams that contribute to scalar masses on one brane and find that the masses are proportional to the compactification scale up to logarithmic corrections, $m^2\propto \left(2\mathrm{}\pi {R)}^{-2}\right[\ln \left(2\mathrm{}\pi {\mathrm{Rm}}_S\right)-1.1],$ where $m_S$ is an ultraviolet cutoff. Thus, for large compactification radii, where this result is valid, the brane scalars acquire a positive mass squared. We also compute the three-loop diagrams relevant to the Casimir energy between the two branes and find $E\propto \left(2\mathrm{}\pi {R)}^{-4}\{\right[\ln \left(2\mathrm{}\pi {\mathrm{Rm}}_S\right)-1.7{]}^2+0.2\mathrm{}\}.$ For large radii, this yields a repulsive Casimir force.