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Mock modularity at work, or black holes in a forest
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Mock modularity at work, or black holes in a forest
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Mock modular forms, first invented by Ramanujan, provide a beautiful generalization of the usual modular forms. In recent years, it was found that they capture generating functions of the number of microstates of BPS black holes appearing in compactifications of string theory with 8 and 16 supercharges. This review describes these results and their applications which range from the actual computation of these generating functions for both compact and non-compact compactification manifolds (encoding, respectively, Donaldson-Thomas and Vafa-Witten topological invariants) to the construction of new non-commutative structures on moduli spaces of Calabi-Yau threefolds.
Forward citations
Cited by 4 Pith papers
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Black Hole Quantum Mechanics and Generalized Error Functions
Derives the general non-holomorphic completion for arbitrary n-center BPS black hole indices using localization on the refined Witten index in supersymmetric quantum mechanics, yielding generalized error functions fro...
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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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Large Order Enumerative Geometry, Black Holes and Black Rings
Numerical study of high-genus GV invariants reveals 5D indices matching BMPV black-hole entropy below a critical angular momentum and black-ring dominance above, with additional phase transitions and growth laws in PT...
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Large Order Enumerative Geometry, Black Holes and Black Rings
Numerical analysis of 5D indices shows a transition from BMPV black hole entropy to black ring entropy at critical angular momentum m, while PT invariants exhibit two further transitions at positive m and DT invariant...
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