Notices of the International Congress of Chinese Mathematicians

Volume 4 (2016)

Number 1

The $\alpha^{\prime}$-expansion of Calabi–Yau compactifications

Pages: 9 – 13

DOI: http://dx.doi.org/10.4310/ICCM.2016.v4.n1.a2

Authors

Katrin Becker (George P. and Cynthia W. Mitchell Institute for Fundamental Physics and Astronomy, Texas A&M University, College Station, Tx., U.S.A.)

Melanie Becker (George P. and Cynthia W. Mitchell Institute for Fundamental Physics and Astronomy, Texas A&M University, College Station, Tx., U.S.A.)

Daniel Robbins (George P. and Cynthia W. Mitchell Institute for Fundamental Physics and Astronomy, Texas A&M University, College Station, Tx., U.S.A.)

Abstract

We consider $\alpha^{\prime}$-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 $\alpha^{\prime}$-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.

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