Gaugino Condensation and the Cosmological Constant
Callum Quigley
TL;DR
The paper investigates whether ${\alpha}'$-corrections and gaugino condensation in the heterotic string can generate a nonzero cosmological constant in four dimensions. Through a detailed reduction of the ${\alpha}'$-corrected ten-dimensional action on a warped product and a gaugino-condensate ansatz, it derives that the four-dimensional cosmological constant $\Lambda$ vanishes to ${\alpha}'^{3}$ and that Minkowski space is the unique maximally symmetric solution within this setup. It then argues—via a generalization of condensates and an all-orders conjecture—that this Minkowski result persists to all orders in the tree-level ${\alpha}'$ expansion, at least for the considered sector. The discussion highlights caveats from threshold (one-loop) corrections and possible AdS constructions, suggesting that effects beyond tree level or outside the ${\alpha}'$-expansion may alter the conclusions and warrant further study.
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.