Linear Chern-Simons-matter theories in the planar limit

We study N\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \mathcal{N} $$\end{document} = 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 ℂℙ1 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. Theadditionoffundamentalmattersisalsodiscussed.