Technically natural vacuum energy at the tip of a supersymmetric teardrop

A minimal supersymmetric braneworld model is presented which has (i) zero classical four-dimensional vacuum curvature, despite the large naive vacuum energy due to contributions from Standard Model particles and (ii) one-(bulk)-loop quantum corrections to the vacuum energy with a size set by the radius of the extra-dimensional spheroid. These corrections are technically natural because a Bogomol’nyi-Prasad-Sommerfield-like relation between the brane tension and $R$ charge—which would have preserved (half of) the bulk supersymmetry—is violated by the requirement that the stabilizing $R$-symmetry gauge flux be quantized. The extra-dimensional geometry is similar to previous rugby-ball geometries, but is simpler in that there is only one brane and so fewer free parameters. Although the sign of the renormalized vacuum energy ends up being the unphysical one for this model (in the limit considered here, where the massive bulk loop is the leading contribution), it serves as an illustrative example of the relevant physics.