Abstract
The existence of de Sitter solutions in string theory is strongly constrained by no-go theorems. We continue our investigation of corrections to the heterotic effective action, with the aim of either strengthening or evading the these constraints. We consider the combined effects of H-flux, gauge bundles, higher derivative corrections and gaugino condensation. The only consistent solutions we find with maximal symmetry in four dimensions are Minkowski spacetimes, ruling out both de Sitter and anti-de Sitter solutions constructed from these ingredients alone.
Highlights
Worldsheet instanton corrections can lead to AdS vacua [9,10,11],1 but dS solutions can be ruled out by an exact worldsheet argument [12]
The only consistent solutions we find with maximal symmetry in four dimensions are Minkowski spacetimes, ruling out both de Sitter and anti-de Sitter solutions constructed from these ingredients alone
We find that the effects of gaugino condensation do not affect previous results: both AdS and dS spacetimes remain excluded in four-dimensional compactifications of the heterotic string, up to O(α′3)
Summary
Our starting point will be the low energy effective action of the heterotic string, including α′ corrections up to quadratic order. The massless field content of the theory consists of a metric gMN , dilaton φ, NS two-form BMN with curvature HMNP , and a Spin(32)/Z2 or E8 × E8 gauge field AM with curvature FMN. Where R is the Ricci scalar and R+AB = dω+AB + ω+AC ∧ ω+CB is the curvature two-form of the spin connection with torsion, ω±AB M. Chern-Simons three-form, and a similar expression holds for CS(ω+). This leads to the well-known Bianchi identity: dH [tr Which must be satisfied, in addition to the equations of motion derived from (2.1), by any solution of the theory.
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