R^4 Corrections to Heterotic M-theory

TL;DR

This paper investigates R^4 higher-derivative corrections in heterotic M-theory, deriving their effects on the Kahler potential, background geometry, and de Sitter vacua, revealing corrections proportional to the Calabi-Yau Euler number.

Contribution

It provides the first explicit solutions for background deformations due to R^4 terms and analyzes their impact on moduli stabilization and vacuum structure in heterotic M-theory.

Findings

Derived the R^4 correction to the Kahler potential and its implications.

Found explicit solutions for background deformations to order kappa^{4/3}.

Identified that corrections are proportional to the Calabi-Yau Euler number.

Abstract

We study R^4 corrections in heterotic M-theory. We derive to order kappa^{4/3} the induced modification to the Kahler potential of the universal moduli and its implications for the soft supersymmetry breaking terms. The soft scalar field masses still remain small for breaking in the T-modulus direction. We investigate the deformations of the background geometry due to the R^4 term. The warp-factor deformation of the background M_4 x CY(3) x S^1/Z_2 can no longer be integrated to a fully non-linear solution, unlike when neglecting higher derivative corrections. We find explicit solutions to order kappa^{4/3} and, in particular, find the expected shift of the Calabi-Yau volume by a constant proportional to the Euler number. We also study the effect induced by the R^4 terms on the de Sitter vacua found previously by balancing two non-perturbative contributions to the superpotential, namely open membrane instantons and gaugino condensation. To order kappa^{4/3} all induced corrections are proportional to the Euler number of the Calabi-Yau three-fold.