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Modular anomaly of BPS black holes
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Generating functions of BPS indices, counting states of D4-D2-D0 black holes in Calabi-Yau compactifications of type IIA string theory and identified with rank 0 Donaldson- Thomas invariants, are examples of mock modular forms. They have a quite complicated modular anomaly expressed as a sum over three different types of trees weighted by generalized error functions and their derivatives. We show that this anomaly can be significantly simplified, which in turn simplfies finding the corresponding mock modular generating functions.
Forward citations
Cited by 2 Pith papers
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Revisiting the Quantum Geometry of Torus-fibered Calabi-Yau Threefolds
The conjectured Jacobi modularity of topological string amplitudes on torus-fibered Calabi-Yau threefolds is derived conditionally from the wave-function property under the relative conifold monodromy, which also maps...
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Mock modularity of Calabi-Yau threefolds
The paper constructs explicit indefinite theta series solving the modular anomaly for rank 0 DT invariants, fixing these generating functions up to modular forms determined by polar terms.
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