Black-holes, topological strings and large N phase transitions

Abstract

The counting of microstates of BPS black-holes on local Calabi-Yau of the form $\mathcal{O}(p-2)\oplus \mathcal{O}(-p)⟶S^2$ is explored by computing the partition function of q-deformed Yang-Mills theory on $S^2$. We obtain, at finite $N$, the instanton expansion of the gauge theory. It can be written exactly as the partition function for U(N) Chern-Simons gauge theory on a Lens space, summed over all non-trivial vacua, plus a tower of non-perturbative instanton contributions. In the large $N$ limit we find a peculiar phase structure in the model. At weak string coupling the theory reduces to the trivial sector and the topological string partition function on the resolved conifold is reproduced in this regime. At a certain critical point, instantons are enhanced and the theory undergoes a phase transition into a strong coupling regime. The transition from the strong coupling phase to the weak coupling phase is of third order.

16 pages, 3 figures; Invited talk given at QG05, Cala Gonone (Italy), September 2005

References in corpus (17)

• Black Hole Attractors and the Topological String
• Black Hole Entropy Function and the Attractor Mechanism in Higher Derivative Gravity
• Exact Counting of Black Hole Microstates
• Black Holes, q-Deformed 2d Yang-Mills, and Non-perturbative Topological Strings
• Precision Counting of Small Black Holes
• Les Houches lectures on matrix models and topological strings
• Asymptotic degeneracy of dyonic N=4 string states and black hole entropy
• Two Dimensional Yang-Mills, Black Holes and Topological Strings
• Exact and Asymptotic Degeneracies of Small Black Holes
• Multi instanton calculus on ALE spaces
• Attractors and the Holomorphic Anomaly
• Stretching the Horizon of a Higher Dimensional Small Black Hole
• BPS Black Hole Degeneracies and Minimal Automorphic Representations
• 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
• A DK Phase Transition in q-Deformed Yang-Mills on S^2 and Topological Strings

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• N=2 Supersymmetric Black Attractors in Six and Seven Dimensions
• Quantum Entanglement of Baby Universes
• Branes, Black Holes and Topological Strings on Toric Calabi-Yau Manifolds
• Instanton on toric singularities and black hole countings
• Chern-Simons matrix models, two-dimensional Yang-Mills theory and the Sutherland model
• Black Holes in Type IIA String on Calabi-Yau Threefolds with Affine ADE Geometries and q-Deformed 2d Quiver Gauge Theories
• Two-dimensional Yang-Mills theory, Painleve equations and the six-vertex model
• Thermodynamics of Noncritical M-Theory and the Topological A-Model
• Topological Strings, Two-Dimensional Yang-Mills Theory and Chern-Simons Theory on Torus Bundles