# Linear Chern-Simons-matter Theories in the Planar Limit

## TL;DR

This paper analyzes ${
m
=3}$ linear Chern-Simons-matter theories in the planar limit, providing explicit formulas for free energy and Wilson loop vevs, and exploring their analytic structure for small cases.

## Contribution

It introduces a unified approach to compute free energy and Wilson loop vevs for all linear theories using a single 1-form on $ ext{CP}^1$, including cases with fundamental matter.

## Key findings

- Explicit formulas for free energy and Wilson loop vevs in terms of a 1-form.
- Detailed analysis of Wilson loop vevs for $n=1$ and $n=2$.
- Inclusion of fundamental matter effects in the theoretical framework.

## Abstract

We study ${\cal N}=3$ 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 $\mathbb{CP}^1$ 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.