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M-theory, topological strings and spinning black holes. (English) Zbl 0985.81081
Summary: We consider M-theory compactification on Calabi-Yau threefolds. The recently discovered connection between the BPS states of wrapped M2 branes and the topological string amplitudes on the threefold is used both as a tool to compute topological string amplitudes at higher genera as well as to unravel the degeneracies and quantum numbers of BPS states. Moduli spaces of \(k\)-fold symmetric products of the wrapped M2 brane play a crucial role. We also show that the topological string partition function is the Calabi-Yau version of the elliptic genus of the symmetric product of \(K3\)’s and use the macroscopic entropy of spinning black holes in 5 dimensions to obtain new predictions for the asymptotic growth of the topological string amplitudes at high genera.

MSC:
81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory
14J81 Relationships with physics
14J32 Calabi-Yau manifolds (algebro-geometric aspects)
83E30 String and superstring theories in gravitational theory
83C57 Black holes
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