Curved four-dimensional spacetime 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 \langle F^a_{\mu\nu}F_a^{\mu\nu}\rangle=F^2 gauge background as well as in an \langle R_{\mu\nu\rho\sigma}R^{\mu\nu\rho\ sigma}\rangle=\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 \langle[F^a_{\mu\nu}]^n[R_{\mu\nu\rho\sigma }]^m\rangle 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 superunification predictions at low energies. (To appear in the Proceedings of the Trieste Spring 94 Workshop)