Analytic torsion for Calabi-Yau threefolds

TL;DR

This paper introduces the BCOV invariant for Calabi-Yau threefolds using analytic torsion, providing explicit formulas and confirming a conjecture for quintic mirror threefolds.

Contribution

It defines the BCOV invariant via analytic torsion and derives explicit formulas on moduli spaces, confirming a key conjecture for quintic mirror threefolds.

Findings

Explicit formula for BCOV invariant on moduli space

Verification of the BCOV invariant conjecture for quintic mirror threefolds

Establishment of the BCOV invariant as a meaningful Calabi-Yau invariant

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.