Refined Black Hole Ensembles and Topological Strings

Abstract

We formulate a refined version of the Ooguri-Strominger-Vafa (OSV) conjecture. The OSV conjecture that Z_{BH} = |Z_{top}|^2 relates the BPS black hole partition function to the topological string partition function Z_{top}. In the refined conjecture, Z_{BH} is the partition function of BPS black holes counted with spin, or more precisely the protected spin character. Z_{top} becomes the partition function of the refined topological string, which is itself an index. Both the original and the refined conjecture are examples of large N duality in the 't Hooft sense. The refined conjecture applies to non-compact Calabi-Yau manifolds only, so the black holes are really BPS particles with large entropy, of order N^2. The refined OSV conjecture states that the refined BPS partition function has a large N dual which is captured by the refined topological string. We provide evidence that the conjecture holds by studying local Calabi-Yau threefolds consisting of line bundles over a genus g Riemann surface. We show that the refined topological string partition function on these geometries is computed by a two-dimensional TQFT. We also study the refined black hole partition function arising from N D4 branes on the Calabi-Yau, and argue that it reduces to a (q,t)-deformed version of two-dimensional SU(N) Yang-Mills. Finally, we show that in the large N limit this theory factorizes to the square of the refined topological string in accordance with the refined OSV conjecture.

49+17 pages, 5 figures

References in corpus (20)

• Stability structures, motivic Donaldson-Thomas invariants and cluster transformations
• The Refined Topological Vertex
• Quantum Entropy Function from AdS(2)/CFT(1) Correspondence
• Toda Theories, Matrix Models, Topological Strings, and N=2 Gauge Systems
• Seiberg-Witten Theory and Random Partitions
• Extended Holomorphic Anomaly in Gauge Theory
• Entropy Function and AdS(2)/CFT(1) Correspondence
• Two Dimensional Yang-Mills, Black Holes and Topological Strings
• Attractors and the Holomorphic Anomaly
• Wall crossing in local Calabi Yau manifolds
• M-theory and a Topological String Duality
• Non-supersymmetric Black Holes and Topological Strings
• BPS Wall Crossing and Topological Strings
• Crossing the Wall: Branes vs. Bundles
• Quantum Entanglement of Baby Universes
• Shift versus Extension in Refined Partition Functions
• Refined Chern-Simons Theory and Knot Homology
• Supersymmetric Partition Functions and a String Theory in 4 Dimensions
• Multiple D4-D2-D0 on the Conifold and Wall-crossing with the Flop
• Motivic Donaldson-Thomas invariants of the conifold and the refined topological vertex

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• Refined stable pair invariants for E-, M- and [p,q]-strings
• Webs of W-algebras
• Refined Chern-Simons Theory and Topological String
• On Extensions of $\widehat{\mathfrak{gl}(m|n)}$ Kac-Moody algebras and Calabi-Yau Singularities
• 4d N=2 supergravity observables from Nekrasov-like partition functions
• q-deformations of two-dimensional Yang-Mills theory: Classification, categorification and refinement
• $T\overline{T}$-deformation of $q$-Yang-Mills theory
• Refined Chern-Simons theory and (q,t)-deformed Yang-Mills theory: Semi-classical expansion and planar limit
• Decomposition and the Gross-Taylor string theory
• Chiral expansion and Macdonald deformation of two-dimensional Yang-Mills theory
• Phase diagram of $q$-deformed Yang-Mills theory on $S^2$ at non-zero $\theta$-angle
• Quantum Black Holes, Elliptic Genera and Spectral Partition Functions
• On Some Computations of Higher Rank Refined Donaldson-Thomas Invariants