Mock modularity of Calabi-Yau threefolds
Abstract
Generating functions $h_r(\tau)$ of D4-D2-D0 BPS indices, appearing in Calabi-Yau compactifications of type IIA string theory and identical to rank 0 Donaldson-Thomas invariants, are known to be higher depth mock modular forms satisfying a specific modular anomaly equation, with depth determined by the D4-brane charge $r$. We develop a method to solve the anomaly equation for arbitrary charges, in terms of indefinite theta series. This allows us to find the generating functions up to modular forms that can be fixed by computing just a finite number of Fourier coefficients of $h_r$.
Fields of Study & Subjects
Black Holes and Theoretical Physics
Algebraic Geometry and Number Theory
Advanced Algebra and Geometry
Publication details
- Journal / source
- Advances in Theoretical and Mathematical Physics
- Volume
- 30
- Issue
- 5
- Pages
- 1231–1347
- Publication date
- 1 January 2026
- Language
- EN