Curved Four-Dimensional Spacetime as Infrared Regulator in Superstring Theories

Abstract

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 $⟨F_{\mu \nu }^a{F}_a^{\mu \nu }⟩=F^2$ gauge background as well as in an $⟨R_{\mu \nu \rho \sigma }{R}^{\mu \nu \rho \sigma }⟩={\mathbb{R}}^2$ 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 $Z(F,\mathbb{R},Q)$ 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 $F=0,\mathbb{R}=0$) 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)

Comments: LateX file, 12pp., CERN-TH.7471/94, LPTENS-94/29