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 DT invariants.
Quantum Background Independence In String Theory
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abstract
Not only in physical string theories, but also in some highly simplified situations, background independence has been difficult to understand. It is argued that the ``holomorphic anomaly'' of Bershadsky, Cecotti, Ooguri, and Vafa gives a fundamental explanation of some of the problems. Moreover, their anomaly equation can be interpreted in terms of a rather peculiar quantum version of background independence: in systems afflicted by the anomaly, background independence does not hold order by order in perturbation theory, but the exact partition function as a function of the coupling constants has a background independent interpretation as a state in an auxiliary quantum Hilbert space. The significance of this auxiliary space is otherwise unknown.
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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 invariants transition to D0-brane dominance.
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The non-perturbative topological string: from resurgence to wall-crossing of DT invariants
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 DT invariants.
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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 invariants transition to D0-brane dominance.