On Cosmological Constants from alpha'-Corrections

TL;DR

This paper investigates whether alpha'-corrections in heterotic string theory can generate a small cosmological constant, concluding that such perturbative effects do not alter the Minkowski vacuum and cannot produce weakly curved AdS_4 solutions.

Contribution

It demonstrates that perturbative alpha'-corrections in heterotic string compactifications do not affect the cosmological constant or produce AdS_4 solutions, emphasizing the need for nonperturbative effects.

Findings

Alpha'-corrections do not generate a cosmological constant in heterotic string compactifications.

Higher order Riemann tensor products vanish in the perturbative regime.

Perturbative alpha'-effects cannot produce weakly curved AdS_4 solutions.

Abstract

We examine to what extent perturbative alpha'-corrections can generate a small cosmological constant in warped string compactifications. Focusing on the heterotic string at lowest order in the string loop expansion, we show that, for a maximally symmetric spacetime, the alpha'-corrected 4D scalar potential has no effect on the cosmological constant. The only relevant terms are instead higher order products of 4D Riemann tensors, which, however, are found to vanish in the usual perturbative regime of the alpha'-expansion. The heterotic string therefore only allows for 4D Minkowski vacua to all orders in alpha', unless one also introduces string loop and/or nonperturbative corrections or allows for curvatures or field strengths that are large in string units. In particular, we find that perturbative alpha'-effects cannot induce weakly curved AdS_4 solutions.