Black Holes, Instanton Counting on Toric Singularities and q-Deformed Two-Dimensional Yang-Mills Theory

Abstract

We study the relationship between instanton counting in N=4 Yang-Mills theory on a generic four-dimensional toric orbifold and the semi-classical expansion of q-deformed Yang-Mills theory on the blowups of the minimal resolution of the orbifold singularity, with an eye to clarifying the recent proposal of using two-dimensional gauge theories to count microstates of black holes in four dimensions. We describe explicitly the instanton contributions to the counting of D-brane bound states which are captured by the two-dimensional gauge theory. We derive an intimate relationship between the two-dimensional Yang-Mills theory and Chern-Simons theory on generic Lens spaces, and use it to show that the correct instanton counting is only reproduced when the Chern-Simons contributions are treated as non-dynamical boundary conditions in the D4-brane gauge theory. We also use this correspondence to discuss the counting of instantons on higher genus ruled Riemann surfaces.

arXiv comment27 pages

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Cited by in corpus (40)

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• Level-rank duality of the U(N) WZW model, Chern-Simons theory, and 2d qYM theory
• Chern-Simons theory on L(p,q) lens spaces and Localization
• Symmetry-breaking vacua and baryon condensates in AdS/CFT
• Factorization of S^3/Z_n partition function
• Coset conformal blocks and N=2 gauge theories
• N=2 gauge theories on toric singularities, blow-up formulae and W-algebrae
• The Volume Conjecture and Topological Strings
• Instantons, Topological Strings and Enumerative Geometry
• Poincare polynomial of moduli spaces of framed sheaves on (stacky) Hirzebruch surfaces
• A brief review of the 2d/4d correspondences
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• Crystal melting on toric surfaces
• Black Holes in Type IIA String on Calabi-Yau Threefolds with Affine ADE Geometries and q-Deformed 2d Quiver Gauge Theories
• $T\overline{T}$-deformation of $q$-Yang-Mills theory
• Beta-ensembles for toric orbifold partition function
• Plethystics and instantons on ALE spaces
• N=2 gauge theories, instanton moduli spaces and geometric representation theory
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• Noncommutative Instantons in Diverse Dimensions
• General modular quantum dilogarithm and beta integrals
• Matrix models and stochastic growth in Donaldson-Thomas theory
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• The Universe as a Set of Topological Fluids with Hierarchy and Fine Tuning of Coupling Constants in Terms of Graph Manifolds
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• Notes On U(1) Instanton Counting On $A_{l-1}$ ALE Spaces