%0 Report
%D 2007
%T Black Holes, Instanton Counting on Toric Singularities and q-Deformed Two-Dimensional Yang-Mills Theory
%A Luca Griguolo
%A Domenico Seminara
%A Richard J. Szabo
%A Alessandro Tanzini
%X 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.
%B Nucl. Phys. B 772 (2007) 1-24
%G en_US
%U http://hdl.handle.net/1963/1888
%1 2347
%2 Mathematics
%3 Mathematical Physics
%$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2006-11-09T10:57:35Z\\nNo. of bitstreams: 1\\nhep-th0610155.pdf: 340757 bytes, checksum: fb3e5bfec5e2a4c15d97a9ca6f2e8a0a (MD5)
%R 10.1016/j.nuclphysb.2007.02.030