Multiple D3-instantons and mock modular forms II
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arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2017
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| _version_ | 1866908445032054784 |
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| author | Alexandrov, Sergei Banerjee, Sibasish Manschot, Jan Pioline, Boris |
| author_facet | Alexandrov, Sergei Banerjee, Sibasish Manschot, Jan Pioline, Boris |
| contents | We analyze the modular properties of D3-brane instanton corrections to the hypermultiplet moduli space in type IIB string theory compactified on a Calabi-Yau threefold. In Part I, we found a necessary condition for the existence of an isometric action of S-duality on this moduli space: the generating function of DT invariants in the large volume attractor chamber must be a vector-valued mock modular form with specified modular properties. In this work, we prove that this condition is also sufficient at two-instanton order. This is achieved by producing a holomorphic action of SL(2,Z) on the twistor space which preserves the holomorphic contact structure. The key step is to cancel the anomalous modular variation of the Darboux coordinates by a local holomorphic contact transformation, which is generated by a suitable indefinite theta series. For this purpose we introduce a new family of theta series of signature (2,n-2), find their modular completion, and conjecture sufficient conditions for their convergence, which may be of independent mathematical interest. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1702_05497 |
| institution | arXiv |
| publishDate | 2017 |
| record_format | arxiv |
| spellingShingle | Multiple D3-instantons and mock modular forms II Alexandrov, Sergei Banerjee, Sibasish Manschot, Jan Pioline, Boris High Energy Physics - Theory Mathematical Physics Algebraic Geometry Number Theory We analyze the modular properties of D3-brane instanton corrections to the hypermultiplet moduli space in type IIB string theory compactified on a Calabi-Yau threefold. In Part I, we found a necessary condition for the existence of an isometric action of S-duality on this moduli space: the generating function of DT invariants in the large volume attractor chamber must be a vector-valued mock modular form with specified modular properties. In this work, we prove that this condition is also sufficient at two-instanton order. This is achieved by producing a holomorphic action of SL(2,Z) on the twistor space which preserves the holomorphic contact structure. The key step is to cancel the anomalous modular variation of the Darboux coordinates by a local holomorphic contact transformation, which is generated by a suitable indefinite theta series. For this purpose we introduce a new family of theta series of signature (2,n-2), find their modular completion, and conjecture sufficient conditions for their convergence, which may be of independent mathematical interest. |
| title | Multiple D3-instantons and mock modular forms II |
| topic | High Energy Physics - Theory Mathematical Physics Algebraic Geometry Number Theory |
| url | https://arxiv.org/abs/1702.05497 |