More large N limits of 3d gauge theories

In this paper we study the large N solution to matrix models describing the partition functions of 3d supersymmetric gauge theories on $S^3$. The model we focus on has a single $U\left(N\right)$ gauge group and fundamental fields, whose number scales with N, also known as the Veneziano limit. The novel point in our model is our choice of masses for the fundamental fields. Instead of vanishing or fixed masses, we consider a linear distribution. We show that the model can still be solved by standard large N techniques and explore the different phases of the model. We also comment about other natural mass distributions. (paper)