  In supersymmetric theories where the lightest supersymmetric particle is the
gravitino the next to lightest supersymmetric particle is typically a long
lived charged slepton. In this paper, following our earlier proposal, we
perform a detailed study of the production of pairs of these particles induced
by the interactions of high energy cosmic neutrinos with nucleons in the earth,
their propagation through the earth and finally their detection in neutrino
telescopes. We investigate the charged slepton energy loss in detail and
establish that the relatively small cross-section for the production of
supersymmetric particles is partially compensated for by the very long range of
these heavy particles. The signal, consisting of two parallel charged tracks
emerging from the earth, is characterized by a track separation of a few
hundred meters. We perform a careful analysis of the main background, coming
from direct di-muon production, and show that it can be separated from the
signal due to its characteristically smaller track separation. We conclude that
neutrino telescopes will complement collider searches in the determination of
the supersymmetry breaking scale, and may even provide the first evidence for
supersymmetry at the weak scale.
