Analytic torsion for Calabi-Yau threefolds

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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Cited by in corpus (2)

• On solutions to Walcher's extended holomorphic anomaly equation
• On the Geometry of Moduli Space of Polarized Calabi-Yau manifolds