arXiv subjects
Publications and source records attributed to Vadim Yasnov.
Following hep-th/0211098 we study the matrix model which describes the topological A-model on T^{*}(S^{3}/\ZZ_p). We show that the resolvent has square root branch cuts and it follows that this is a p cut single matrix model. We solve for the resolvent and find the spectral curve. We comment on how this is related to large N transitions and mirror symmetry.
We demonsrate that the spectral curve of the matrix model for Chern-Simons theory on the Lens space S^{3}/\ZZ_p is precisely the Riemann surface which appears in the mirror to the blownup, orbifolded conifold. This provides the first check of the $A$-model large $N$ duality for T^{*}(S^{3}/\ZZ_p), p>2.
For matrix models with measure on the Lie algebra of SO/Sp, the sub-leading free energy is given by F_{1}(S)=\pm{1/4}\frac{\del F_{0}(S)}{\del S}. Motivated by the fact that this relationship does not hold for Chern-Simons theory on S^{3}, we calculate the sub-leading free energy in the matrix model for this theory, which is a Gaussian matrix model with Haar measure on the group SO/Sp. We derive a quantum loop equation for this matrix model and then find that F_{1} is an integral of the leading order resolvent over the spectral curve. We explicitly calculate this integral for quadratic potential and find agreement with previous studies of SO/Sp Chern-Simons theory.