Instanton on toric singularities and black hole countings

Details Instanton on toric singularities and black hole countings Instanton on toric singularities and black hole countings

2006-10-13

arxiv.org/abs/hep-th/0610154v3

JHEP0612:073,2006

Physics

High Energy Physics

High Energy Physics - Theory

29 pages, 3 fig Section 5 is improved by the inclusion of a detailed comparison between the instanton partition function and t

Scientific paper

10.1088/1126-6708/2006/12/073

We compute the instanton partition function for ${\cal N}=4$ U(N) gauge theories living on toric varieties, mainly of type $\R^4/\Gamma_{p,q}$ 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.

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