Multiple D3-instantons and mock modular forms II

Abstract

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.

24+24 pages

References in corpus (9)

• String loop corrected hypermultiplet moduli spaces
• A Farey Tail for Attractor Black Holes
• Nonperturbative corrections to 4D string theory effective actions from SL(2,Z) duality and supersymmetry
• D-instantons and twistors
• The M5-Brane Elliptic Genus: Modularity and BPS States
• Quantum mirror symmetry and twistors
• S-duality in Twistor Space
• Dualities and fivebrane instantons
• Fivebrane instantons in Calabi-Yau compactifications

Cited by in corpus (17)

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• Scaling Black Holes and Modularity
• Hypermultiplet metric and NS5-instantons
• Squashed Toric Manifolds and Higher Depth Mock Modular Forms
• Three Avatars of Mock Modularity
• Mock modularity at work, or black holes in a forest
• Quantum Modular $\hat{Z}{}^G$-Invariants
• Modular anomaly of BPS black holes
• S-duality and the universal isometries of instanton corrected q-map spaces
• Quantum Curve for strip geometries, Topological Recursion and open GW/DT invariants
• S-duality and the universal isometries of q-map spaces
• Quantum TBA for refined BPS indices