R^4 Corrections and Flux Superpotential in Heterotic M-theory
I will describe two kinds of corrections to the previously known
effective action of heterotic M-theory. The first is due to taking into
account the 11d R^4 term. This results in a new contribution to the Kahler
potential of the four-dimensional effective theory. The second comes from
the flux-generated superpotential. To derive systematically the form of
this superpotential, one has to use the approach of group structures. It
is essential to consider SU(3), not G_2, structure on the internal 7d
manifold. Finally, I will address the issue of how these corrections
affect the existence of dS vacua in heterotic M-theory, which were
originally found by balancing open membrane instanton effects and
gaugino condensation.