  Using recent advances in the understanding of non-critical strings, we
construct a unique, conformally invariant continuation to off-shell momenta of
Polyakov amplitudes in critical string theory. Three-point amplitudes are
explicitly calculated. These off-shell amplitudes possess some unusual,
apparently stringy, characteristics, which are unlikely to be reproduced in a
string field theory. Thus our results may be an indication that some
fundamentally new formulation, other than string field theory, will be required
to extend our understanding of critical strings beyond the Polyakov path
integral.
