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 and DT invariants.
Some Details On The Gopakumar-Vafa and Ooguri-Vafa Formulas
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abstract
The Gopakumar-Vafa (GV) formula expresses certain couplings that arise in Type IIA compactification to four dimensions on a Calabi-Yau manifold in terms of a counting of BPS states in M-theory. The couplings in question have applications to topological strings and supersymmetric black holes. In this paper, we reconsider the GV formula, taking a close look at the Schwinger-like computation that was suggested in the original GV work. The goal is to understand the background that must be used in this computation, the role played by the extended supersymmetry of this background, and how the computation gives a holomorphic result though superficially depending only on particle masses. We also examine in a similar way the Ooguri-Vafa (OV) formula, which is an extension of the GV formula to include D4-branes.
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UNVERDICTED 2representative citing papers
Extends operator formalism of closed topological strings to derive all-order trans-series solutions for real topological strings, with disk invariants as Stokes constants and numerical checks on local P2.
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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 and DT invariants.
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Non-Perturbative Real Topological Strings
Extends operator formalism of closed topological strings to derive all-order trans-series solutions for real topological strings, with disk invariants as Stokes constants and numerical checks on local P2.