5 research outputs found
The Spectral Curve of the Lens Space Matrix Model
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.Comment: 25 pages, 2 figures, typos corrected, comments adde
Large N Duality, Lens Spaces and the Chern-Simons Matrix Model
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 -model large duality for T^{*}(S^{3}/\ZZ_p), p>2.Comment: 12 pages, 2 figure
Chern-Simons Matrix Models and Unoriented Strings
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.Comment: 28 pages, 2 figures V2: re-organised for clarity, results unchange