Curved Four-Dimensional Spacetime as Infrared Regulator in Superstring Theories

TL;DR

This work introduces curved four-dimensional spacetime as an infrared regulator for string theory, constructing exact ${\hat c}=4$ superstring backgrounds with a curvature-induced mass gap $\mu^2=Q^2/4$ where $Q^2=2/(k+2)$. It develops modular-invariant partition functions for curved backgrounds $W_k^{(4)}\otimes K^{(6)}$, and extends them to deformations by constant gauge field strength $F$ and curvature $\cal R$, analyzed via a Lorentzian lattice boost that yields integrated correlators $\langle F^nR^m\rangle$, notably the gauge-coupling correction $Z_{2,0}(Q)$. The approach yields an IR- and UV-finite, regulator-dependent yet modular-invariant framework to compute string threshold corrections as functions of moduli, with backreaction treated exactly. Overall, curvature acts as a physically well-defined regulator that preserves a form of spacetime supersymmetry and allows unambiguous one-loop calculations essential for string superunification.

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 $\langle F^a_{μν}F_a^{μν}\rangle=F^2$ gauge background as well as in an $\langle R_{μνρσ}R^{μνρσ}\rangle=\R^2$ gravitational background and we show that the non-zero curvature, $Q^2=2/(k+2)$, of the spacetime provides an infrared regulator for all $\langle[F^a_{μν}]^n[R_{μνρσ}]^m\rangle$ 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)