  Motivated by recent studies of supersymmetry in higher-dimensional spaces, we
discuss the experimental signatures of a superlight gravitino, mass < 0.001 eV.
We concentrate on the process (e- gamma -> selectronR gravitino) as a probe of
supersymmetry, where a single heavy superpartner and a superlight gravitino are
produced. The fact that there is only one heavy superpartner in the final state
in this process would require a lower center-of-mass energy for on-shell
production compared to conventional pair production. For instance, for a 500
GeV machine, we find that a positive signal will be found if the supersymmetry
breaking scale is less than about 2 TeV. If no positive signal is found, this
process puts a bound on the supersymmetry breaking scale.
