01271nas a2200133 4500008004300000245007300043210006800116520083300184100001801017700001901035700002301054700002401077856003601101 2010 en_Ud 00aChern-Simons theory on L(p,q) lens spaces and Gopakumar-Vafa duality0 aChernSimons theory on Lpq lens spaces and GopakumarVafa duality3 aWe 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.1 aBrini, Andrea1 aGriguolo, Luca1 aSeminara, Domenico1 aTanzini, Alessandro uhttp://hdl.handle.net/1963/293801457nas a2200133 4500008004300000245010800043210006900151520097900220100001901199700002301218700002201241700002401263856003601287 2007 en_Ud 00aBlack Holes, Instanton Counting on Toric Singularities and q-Deformed Two-Dimensional Yang-Mills Theory0 aBlack Holes Instanton Counting on Toric Singularities and qDefor3 aWe 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.1 aGriguolo, Luca1 aSeminara, Domenico1 aSzabo, Richard J.1 aTanzini, Alessandro uhttp://hdl.handle.net/1963/1888