Linear Chern-Simons-matter theories in the planar limit

Abstract

We study N = 3 linear Chern-Simons-matter theories in the planar limit. The matter content of the theory is depicted by a linear-shape diagram with n nodes and n − 1 links for any n. The free energy and the vevs of BPS Wilson loops are given in terms of a single 1-form on CP 1 which can be determined explicitly for all linear theories. The analytic structure of the vevs of the Wilson loops is investigated in detail for n = 1 and n = 2. The addition of fundamental matters is also discussed.

The large-N partition function for non-parity-invariant Chern-Simons-matter theories

“…For example, the genus zero free energy F 0 (λ) can be obtained directly from the planar resolvent. Although most investigations have focused on two node quivers, matrix resolvent techniques have been applied to more general necklace and linear quivers [27,28]. Of course, for a complete picture to emerge, there are not only higher genus but also non-perturbative in N corrections that need to be taken into account.…”