Flops and the S-duality conjecture

Abstract

We prove the transformation formula of Donaldson-Thomas (DT) invariants counting two dimensional torsion sheaves on Calabi-Yau 3-folds under flops. The error term is described by the Dedekind eta function and the Jacobi theta function, and our result gives evidence of a 3-fold version of Vafa-Witten's S-duality conjecture. As an application, we prove a blow-up formula of DT type invariants on the total spaces of canonical line bundles on smooth projective surfaces. It gives an analogue of the similar blow-up formula in the original S-duality conjecture by Yoshioka, Li-Qin and Göttsche.

36 pages

References in corpus (4)

• The M5-Brane Elliptic Genus: Modularity and BPS States
• Examples of M5-Brane Elliptic Genera
• Multiple D4-D2-D0 on the Conifold and Wall-crossing with the Flop
• Counting curves on surfaces in Calabi-Yau 3-folds

Cited by in corpus (3)

• Multiple D3-instantons and mock modular forms I
• Multiple D3-instantons and mock modular forms II
• Vertical D4-D2-D0 bound states on K3 fibrations and modularity