Chern-Simons Matrix Models and Unoriented Strings

Abstract

For matrix models with measure on the Lie algebra of SO/Sp, the sub-leading free energy is given by F 1 (S) = ± 1 4 ∂F 0 (S) ∂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.

Large N Duality, Lens Spaces and the Chern-Simons Matrix Model

“…For the case p = 2 the partition function of this matrix model was calculated perturbatively and was shown to agree with the Kodaira-Spencer theory [9] predictions from the large N dual geometry, providing solid evidence for the proposed duality. For CS theory on S 3 the matrix model was solved to all genus using orthogonal polynomials in [10] and the orientifold of the conifold was studied in [11].…”

Matrix model of Chern–Simons matter theories beyond the spherical limit

“…There is a straight-forward generalization of the presented formulation to a different gauge group [53] or two matrices. This generalization to two matrices is important for the application to higher supersymmetric Chern-Simons matter theories such as the ABJM theory [54].…”

Matrix Models and Topological Strings

“…The result (4.33) can be derived as well from the perturbation series [35,34], but the existence of a matrix model description of Chern-Simons theory turns out to be useful in other situations as well. For example, one can easily write a matrix integral for Chern-Simons theory for other gauge groups [53], and the corresponding models have been analyzed in [37]. Moreover, the matrix representation of Chern-Simons partition functions can be extended to lens spaces and Seifert spaces, and provides a useful way to study perturbative expansions around nontrivial flat connections.…”