Instanton on toric singularities and black hole countings

Abstract

We compute the instanton partition function for $\mathcal{N}=4$ U(N) gauge theories living on toric varieties, mainly of type ${\mathbb{R}}^4/{\Gamma }_{p,q}$ including $A_{p-1}$ or $O_{\PP_1}(-p)$ surfaces. The results provide microscopic formulas for the partition functions of black holes made out of D4-D2-D0 bound states wrapping four-dimensional toric varieties inside a Calabi-Yau. The partition function gets contributions from regular and fractional instantons. Regular instantons are described in terms of symmetric products of the four-dimensional variety. Fractional instantons are built out of elementary self-dual connections with no moduli carrying non-trivial fluxes along the exceptional cycles of the variety. The fractional instanton contribution agrees with recent results based on 2d SYM analysis. The partition function, in the large charge limit, reproduces the supergravity macroscopic formulae for the D4-D2-D0 black hole entropy.

29 pages, 3 fig Section 5 is improved by the inclusion of a detailed comparison between the instanton partition function and the D4-D2-D0 black hole entropy formula coming from supergravity

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• Instanton moduli spaces and bases in coset conformal field theory
• Gauge Theories on ALE Space and Super Liouville Correlation Functions
• Symmetry-breaking vacua and baryon condensates in AdS/CFT
• Parafermionic Liouville field theory and instantons on ALE spaces
• Exact results for $\mathcal{N}=2$ supersymmetric gauge theories on compact toric manifolds and equivariant Donaldson invariants
• N=2 gauge theories on toric singularities, blow-up formulae and W-algebrae
• Scheme dependence of instanton counting in ALE spaces
• Poincare polynomial of moduli spaces of framed sheaves on (stacky) Hirzebruch surfaces
• A brief review of the 2d/4d correspondences
• Coset conformal field theory and instanton counting on C^2/Z_p
• Crystal melting on toric surfaces
• 5d gauge theories on orbifolds and 4d 't Hooft line indices
• Noncommutative Instantons in Diverse Dimensions
• The light asymptotic limit of conformal blocks in $\mathcal{N}=1$ super Liouville field theory
• The ADHM-like Constructions for Instantons on CP^2 and Three Dimensional Gauge Theories
• A Note on q-Deformed Two-Dimensional Yang-Mills and Open Topological Strings