Analytic torsion for Borcea-Voisin threefolds

TL;DR

This paper explores the BCOV invariants of Borcea-Voisin threefolds, relating them to torsion invariants of K3 surfaces with involution and comparing invariants between orbifolds and their resolutions.

Contribution

It establishes a link between BCOV invariants of Borcea-Voisin threefolds and torsion invariants of K3 surfaces with involution, and introduces BCOV invariants for abelian Calabi-Yau orbifolds.

Findings

Identification of BCOV invariants with torsion invariants for K3 surfaces with involution

Comparison of BCOV invariants between orbifolds and crepant resolutions

Introduction of BCOV invariants for abelian Calabi-Yau orbifolds

Abstract

In their study of genus-one string amplitude, Bershadsky-Cecotti-Ooguri-Vafa discovered a remarkable identification between holomorphic Ray-Singer torsion and instanton numbers for Calabi-Yau threefolds. The holomorphic torsion invariant for Calabi-Yau threefolds corresponding to the genus-one string amplitude is called BCOV invariant. In this paper, we establish an identification between the BCOV invariants of Borcea-Voisin threefolds and another holomorphic torsion invariants for K3 surfaces with involution. We also introduce BCOV invariants for abelian Calabi-Yau orbifolds. Between Borcea-Voisin orbifold and its crepant resolution, we compare their BCOV invariants.