Supersymmetry, Large Extra Dimensions and the Gravitino Conjecture

Abstract

We investigate whether the absence of experimental signals for supersymmetry and extra dimensions can be understood as a correlated phenomenon. Assuming the Gravitino Conjecture, we study the relation between the gravitino mass and the Kaluza-Klein scale in four-dimensional $\mathcal{N}=1$ supergravity from Type II compactifications with large extra dimensions. We parametrize the scaling of the full internal volume with respect to that of a large $p$-cycle through an anisotropy exponent $α$, and derive the corresponding volume contributions to the Kähler potential. This leads to constraints on the scaling exponent $n$, linking the gravitino mass to the KK scale, and on the effective number $αp$ of large dimensions. We find that the linear relation $n=1$ is compatible only with one or two large extra dimensions, precisely the cases that can still be probed at micron distances. In such scenarios, micron-sized extra dimensions imply a light gravitino and gauge-mediated supersymmetry breaking, whereas gravity mediation corresponds to compactification scales beyond current experimental reach.