On Cosmological Constants from alpha'-Corrections

TL;DR

The paper proves a no-go for generating a small cosmological constant from perturbative α′-corrections in heterotic string compactifications with maximal 4D symmetry. By analyzing the dilaton and 4D Einstein equations under a perturbative α′-expansion, it derives a relation of the form $Λ = ∑_{m,n>0} c_{mn} α′^{m} Λ^{n}$, which forces $Λ=0$ to all orders in perturbation theory in the absence of loop or nonperturbative effects. At leading order, the result reads $Λ = α′( c_{11} Λ + c_{12} Λ^2 ) + O(α′^2)$ with coefficients given by internal integrals that vanish for perturbative backgrounds, ruling out perturbatively small AdS4 vacua. The authors discuss possible loopholes, including loop/nonperturbative corrections, spacetime-filling fluxes, and regimes where the effective potential description breaks down, highlighting the connection to the Dine–Seiberg problem and the need for nonperturbative or strongly curved inputs to obtain nonzero Λ.

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.