CURVED 4-DIMENSIONAL SPACE-TIME AS INFRARED REGULATOR IN SUPERSTRING THEORIES

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 spacetime provides an infrared regulator for all [[F-mu nu(a)](n)[R(mu nu rho sigma)](m)] correlation functions. The string one-loop partition function Z(F, R, Q) can be exactly computed, and it is IR and UV finite. For Q small we have thus obtained an IR regularization, consistent with spacetime supersymmetry (when F = 0, R = 0) and modular invariance. Thus, it can be used to determine, without any infrared ambiguities, the one-loop string radiative corrections on gravitational, gauge or Yukawa couplings necessary for the string superunificatinn predictions at low energies.