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Analytic torsion for Calabi-Yau threefolds

Hao Fang·Zhiqin Lu·Ken-Ichi Yoshikawa
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Abstract

After Bershadsky-Cecotti-Ooguri-Vafa, we introduce an invariant of Calabi-Yau threefolds, which we call the BCOV invariant and which we obtain using analytic torsion. We give an explicit formula for the BCOV invariant as a function on the compactified moduli space, when it is isomorphic to a projective line. As a corollary, we prove the formula for the BCOV invariant of quintic mirror threefolds conjectured by Bershadsky-Cecotti-Ooguri-Vafa.

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Hao Fang, Zhiqin Lu, Ken-Ichi Yoshikawa. 2006-02-02. Analytic torsion for Calabi-Yau threefolds. https://arxiv.org/abs/math/0601411

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