Analytic Torsion for Borcea–Voisin Threefolds

Abstract

In their study of genus-one string amplitude F ₁, Bershadsky–Cecotti–Ooguri–Vafa discovered a remarkable identification between holomorphic Ray–Singer torsion and instanton numbers for Calabi–Yau threefolds. The holomorphic torsion invariant of Calabi–Yau threefolds corresponding to F ₁ 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 K ₃ 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.