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Black Holes and Large Order Quantum Geometry

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arxiv 0704.2440 v2 pith:PA44GJMI submitted 2007-04-18 hep-th

Black Holes and Large Order Quantum Geometry

classification hep-th
keywords blackholesentropylargemicroscopicobtainedtheoryvarious
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
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We study five-dimensional black holes obtained by compactifying M theory on Calabi-Yau threefolds. Recent progress in solving topological string theory on compact, one-parameter models allows us to test numerically various conjectures about these black holes. We give convincing evidence that a microscopic description based on Gopakumar-Vafa invariants accounts correctly for their macroscopic entropy, and we check that highly nontrivial cancellations -which seem necessary to resolve the so-called entropy enigma in the OSV conjecture- do in fact occur. We also study analytically small 5d black holes obtained by wrapping M2 branes in the fiber of K3 fibrations. By using heterotic/type II duality we obtain exact formulae for the microscopic degeneracies in various geometries, and we compute their asymptotic expansion for large charges.

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Cited by 4 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. The non-perturbative topological string: from resurgence to wall-crossing of DT invariants

    hep-th 2026-04 unverdicted novelty 8.0

    An isomorphism is shown between the algebra of alien derivatives acting on the topological string partition function and the Kontsevich-Soibelman Lie algebra, linking resurgence to DT wall-crossing with numerical matc...

  2. The non-perturbative topological string: from resurgence to wall-crossing of DT invariants

    hep-th 2026-04 unverdicted novelty 7.0

    Links resurgence of the topological string partition function to DT wall-crossing via an isomorphism of alien derivative algebras to the Kontsevich-Soibelman Lie algebra, with Borel singularities matched to specific D...

  3. Large Order Enumerative Geometry, Black Holes and Black Rings

    hep-th 2026-05 unverdicted novelty 6.0

    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...

  4. Large Order Enumerative Geometry, Black Holes and Black Rings

    hep-th 2026-05 unverdicted novelty 6.0

    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...