Branes, Black Holes and Topological Strings on Toric Calabi-Yau Manifolds

Abstract

We develop means of computing exact degerenacies of BPS black holes on toric Calabi-Yau manifolds. We show that the gauge theory on the D4 branes wrapping ample divisors reduces to 2D q-deformed Yang-Mills theory on necklaces of P^1's. As explicit examples we consider local P^2, P^1 x P^1 and A_k type ALE space times C. At large N the D-brane partition function factorizes as a sum over squares of chiral blocks, the leading one of which is the topological closed string amplitude on the Calabi-Yau. This is in complete agreement with the recent conjecture of Ooguri, Strominger and Vafa.

arXiv comment50 pages, 6 figures, harvmac

References in corpus (22)

• A Strong Coupling Test of S-Duality
• Black Hole Entropy in M-Theory
• Black Hole Attractors and the Topological String
• The Topological Vertex
• Topological Strings and Integrable Hierarchies
• Exact Counting of Black Hole Microstates
• Corrections to macroscopic supersymmetric black-hole entropy
• Black Holes, q-Deformed 2d Yang-Mills, and Non-perturbative Topological Strings
• Precision Counting of Small Black Holes
• Matrix Model as a Mirror of Chern-Simons Theory
• Instantons on D-branes
• Macroscopic entropy formulae and non-holomorphic corrections for supersymmetric black holes
• Supersymmetric Yang-Mills Theory On A Four-Manifold
• E-Strings and N=4 Topological Yang-Mills Theories
• All Loop Topological String Amplitudes From Chern-Simons Theory
• Exact and Asymptotic Degeneracies of Small Black Holes
• Exact Black Hole Degeneracies and the Topological String
• Black Holes, Elementary Strings and Holomorphic Anomaly
• Topological strings and large N phase transitions II: Chiral expansion of q-deformed Yang-Mills theory
• Phase transitions in q-deformed 2d Yang-Mills theory and topological strings
• Topological strings and large N phase transitions I: Nonchiral expansion of q-deformed Yang-Mills theory
• Black-holes, topological strings and large N phase transitions

Cited by in corpus (15)

• Borel and Stokes Nonperturbative Phenomena in Topological String Theory and c=1 Matrix Models
• Cohomological Hall algebras, vertex algebras and instantons
• Webs of W-algebras
• Seiberg-Witten theory and matrix models
• Level-rank duality of the U(N) WZW model, Chern-Simons theory, and 2d qYM theory
• On Extensions of $\widehat{\mathfrak{gl}(m|n)}$ Kac-Moody algebras and Calabi-Yau Singularities
• Refined Black Hole Ensembles and Topological Strings
• q-deformations of two-dimensional Yang-Mills theory: Classification, categorification and refinement
• Two-dimensional crystal melting and D4-D2-D0 on toric Calabi-Yau singularities
• Black String Entropy and Fourier-Mukai Transform
• Qubits from Black Holes in M-theory on K3 Surface
• Vertical D4-D2-D0 bound states on K3 fibrations and modularity
• Black Hole Partition Function using Hybrid Formalism of Superstrings
• Qubit and Fermionic Fock Spaces from Type II Superstring Black Holes
• A Note on q-Deformed Two-Dimensional Yang-Mills and Open Topological Strings