Donaldson-Thomas invariants are the mathematical incarnation of BPS indices counting black hole micro-states in string compactifications. They are notoriously difficult to compute, and subject to wall-crossing phenomena. String dualities predict that generating series of DT invariants counting D4-D2-D0 black holes should have modular (or more generally mock modular) behavior. For one-parameter CY threefolds such as the quintic, one may compute the first few terms in the generating series using vanishing theorems and wall-crossing formulae,and find a unique modular completion. This in turn allows to predict new Gopakumar-Vafa invariants, and determine the topological string amplitude to higher genus than hitherto possible. Based on work in collaboration with Sergey Alexandrov, Soheyla Feyzbakhsh, Albrecht Klemm and Thorsten Schimmanek.
Boris Pioline (LPTHE - Sorbonne Université)
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15 июн 2024
