  Off-shell interactions for localized closed-string tachyons in C/Z_N
superstring backgrounds are analyzed and a conjecture for the effective height
of the tachyon potential is elaborated. At large N, some of the relevant
tachyons are nearly massless and their interactions can be deduced from the
S-matrix. The cubic interactions between these tachyons and the massless fields
are computed in a closed form using orbifold CFT techniques. The cubic
interaction between nearly-massless tachyons with different charges is shown to
vanish and thus condensation of one tachyon does not source the others. It is
shown that to leading order in N, the quartic contact interaction vanishes and
the massless exchanges completely account for the four point scattering
amplitude. This indicates that it is necessary to go beyond quartic
interactions or to include other fields to test the conjecture for the height
of the tachyon potential.
