Mock modularity of Calabi-Yau threefolds
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866929687552327680 |
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| author | Alexandrov, Sergei Bendriss, Khalil |
| author_facet | Alexandrov, Sergei Bendriss, Khalil |
| contents | Generating functions $h_r(τ)$ 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 $h_r$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_17699 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Mock modularity of Calabi-Yau threefolds Alexandrov, Sergei Bendriss, Khalil High Energy Physics - Theory Mathematical Physics Algebraic Geometry Number Theory Generating functions $h_r(τ)$ 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 $h_r$. |
| title | Mock modularity of Calabi-Yau threefolds |
| topic | High Energy Physics - Theory Mathematical Physics Algebraic Geometry Number Theory |
| url | https://arxiv.org/abs/2411.17699 |