@article {2010,
title = {Chern-Simons theory on L(p,q) lens spaces and Gopakumar-Vafa duality},
journal = {J. Geom. Phys. 60 (2010) 417-429},
number = {SISSA;56/2008/FM},
year = {2010},
abstract = {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.},
doi = {10.1016/j.geomphys.2009.11.006},
url = {http://hdl.handle.net/1963/2938},
author = {Andrea Brini and Luca Griguolo and Domenico Seminara and Alessandro Tanzini}
}
@article {2007,
title = {Black Holes, Instanton Counting on Toric Singularities and q-Deformed Two-Dimensional Yang-Mills Theory},
number = {SISSA;61/2006/FM},
year = {2007},
abstract = {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.},
doi = {10.1016/j.nuclphysb.2007.02.030},
url = {http://hdl.handle.net/1963/1888},
author = {Luca Griguolo and Domenico Seminara and Richard J. Szabo and Alessandro Tanzini}
}