M-Theory, Topological Strings and Spinning Black Holes

Abstract

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.

75 pages, 2 figures

References in corpus (5)

• Mirror Symmetry, Mirror Map and Applications to Calabi-Yau Hypersurfaces
• c=1 String as the Topological Theory of the Conifold
• Topological Field Theory and Rational Curves
• Counting higher genus curves in a Calabi-Yau manifold
• Enumeration of $n$-fold tangent hyperplanes to a surface

Cited by in corpus (6)

• New Connections Between 4D and 5D Black Holes
• Integrability of the holomorphic anomaly equations
• Three questions in Gromov-Witten theory
• Hilbert schemes of points on a locally planar curve and the Severi strata of its versal deformation
• Topological String Partition Functions as Equivariant Indices
• Gopakumar-Vafa BPS invariants, Hilbert schemes and quasimodular forms. I