TY - JOUR
T1 - Chern-Simons theory on L(p,q) lens spaces and Gopakumar-Vafa duality
JF - J. Geom. Phys. 60 (2010) 417-429
Y1 - 2010
A1 - Andrea Brini
A1 - Luca Griguolo
A1 - Domenico Seminara
A1 - Alessandro Tanzini
AB - 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.
UR - http://hdl.handle.net/1963/2938
U1 - 1762
U2 - Mathematics
U3 - Mathematical Physics
ER -
TY - RPRT
T1 - Black Holes, Instanton Counting on Toric Singularities and q-Deformed Two-Dimensional Yang-Mills Theory
Y1 - 2007
A1 - Luca Griguolo
A1 - Domenico Seminara
A1 - Richard J. Szabo
A1 - Alessandro Tanzini
AB - 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.
JF - Nucl. Phys. B 772 (2007) 1-24
UR - http://hdl.handle.net/1963/1888
U1 - 2347
U2 - Mathematics
U3 - Mathematical Physics
ER -