The alpha'-Expansion of Calabi-Yau Compactifications

TL;DR

This paper reviews alpha'-corrections to Calabi-Yau compactifications in string theory, showing that these corrections modify the internal manifold's structure from Ricci-flat Calabi-Yau to SU(3)-structure manifolds, consistent across worldsheet and effective field theory approaches.

Contribution

It clarifies how alpha'-corrections alter Calabi-Yau manifolds, demonstrating their transition to SU(3)-structure manifolds in string compactifications.

Findings

Calabi-Yau manifolds remain Calabi-Yau with alpha'-corrections but are no longer Ricci flat.

Alpha'-corrections lead to SU(3)-structure manifolds instead of strict SU(3)-holonomy.

Results are consistent between worldsheet and space-time effective field theory analyses.

Abstract

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.