Curved Four-Dimensional Spacetime as Infrared Regulator in Superstring Theories

TL;DR

This paper constructs exact superstring solutions with curved four-dimensional spacetime, demonstrating that spacetime curvature acts as an infrared regulator, enabling precise one-loop calculations of string corrections without infrared ambiguities.

Contribution

It introduces a new class of stable superstring solutions with curved spacetime that serve as an IR regulator, allowing exact one-loop partition function computations in non-trivial backgrounds.

Findings

Spacetime curvature provides an IR cutoff for correlation functions.

The one-loop partition function is exactly computed and finite.

The method maintains spacetime supersymmetry and modular invariance.

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 $\langle F^a_{\mu\nu}F_a^{\mu\nu}\rangle=F^2$ 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)