We construct a new class of exact and stable superstring solutions in
which our four-dimensional spacetime is taken to be curved. We derive
in this space the full one-loop partition function in the presence of
non-zero [(Fmu nuFamu nu)-F-a] = F-2 gauge background as well as in an
[R(mu nu rho sigma)R(mu nu rho sigma] = R?2 gravitational background
and we show that the non-zero curvature, Q?2 = 2/(k+2), of the spaceti
me provides an infrared regulator for all [[F-mu nu(a)](n)[R(mu nu rho
sigma)](m)] correlation functions. The string one-loop partition func
tion Z(F, R, Q) can be exactly computed, and it is IR and UV finite. F
or Q small we have thus obtained an IR regularization, consistent with
spacetime supersymmetry (when F = 0, R = 0) and modular invariance. T
hus, it can be used to determine, without any infrared ambiguities, th
e one-loop string radiative corrections on gravitational, gauge or Yuk
awa couplings necessary for the string superunificatinn predictions at
low energies.