The alpha'-Expansion of Calabi-Yau Compactifications

We consider alpha'-corrections to Calabi-Yau compactifications of type II string theory. These were discussed from the string worldsheet approach many years ago in terms of supersymmetric non-linear sigma-models by Nemeschansky and Sen as well as Gross and Witten. There it was shown that once alpha'-corrections are included, the internal manifold solving the string equations of motion is still Calabi-Yau though not Ricci flat. In this brief note we review these results and compare with a space-time effective field theory approach, in which we show that SU(3)-holonomy manifolds become SU(3)-structure manifolds once such corrections are included.