R4 corrections to heterotic M-theory

We study R4 corrections in heterotic M-theory. We derive to order κ4/3 the induced modification to the Kähler 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 R4 term. The warp-factor deformation of the background M4×CY(3)×S1/Z2 can no longer be integrated to a fully non-linear solution, unlike when neglecting higher derivative corrections. We find explicit solutions to order κ4/3 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 R4 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 κ4/3 all induced corrections are proportional to the Euler number of the Calabi-Yau three-fold.