%0 Journal Article
%J J. Geom. Phys. 60 (2010) 417-429
%D 2010
%T Chern-Simons theory on L(p,q) lens spaces and Gopakumar-Vafa duality
%A Andrea Brini
%A Luca Griguolo
%A Domenico Seminara
%A Alessandro Tanzini
%X We consider aspects of Chern-Simons theory on L(p,q) lens spaces and its relation with matrix models and topological string theory on Calabi-Yau threefolds, searching for possible new large N dualities via geometric transition for non-SU(2) cyclic quotients of the conifold. To this aim we find, on one hand, some novel matrix integral representations of the SU(N) CS partition function in a generic flat background for the whole L(p,q) family and provide a solution for its large N dynamics; on the other, we perform in full detail the construction of a family of would-be dual closed string backgrounds via conifold geometric transition from T^*L(p,q). We can then explicitly prove that Gopakumar-Vafa duality in a fixed vacuum fails in the case q>1, and briefly discuss how it could be restored in a non-perturbative setting.
%B J. Geom. Phys. 60 (2010) 417-429
%G en_US
%U http://hdl.handle.net/1963/2938
%1 1762
%2 Mathematics
%3 Mathematical Physics
%$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-09-12T16:01:18Z\\nNo. of bitstreams: 1\\n0809.1610v1.pdf: 287875 bytes, checksum: feadff501b37135585a6f62946b628de (MD5)
%R 10.1016/j.geomphys.2009.11.006
%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