  We study two dimensional $\mathcal{N} = (2, 2)$ Landau-Ginzburg models with
tensor valued superfields with the aim of constructing large central charge
superconformal field theories which are solvable using large $N$ techniques. We
demonstrate the viability of such constructions and motivate the study of
anisotropic tensor models. Such theories are a novel deformation of tensor
models where we break the continuous symmetries while preserving the large $N$
solvability. Specifically, we examine theories with superpotentials involving
tensor contractions chosen to pick out melonic diagrams. The anisotropy is
introduced by further biasing individual terms by different coefficients, all
of the same order, to retain large $N$ scaling. We carry out a detailed
analysis of the resulting low energy fixed point and comment on potential
applications to holography. Along the way we also examine gauged versions of
the models (with partial anisotropy) and find generically that such theories
have a non-compact Higgs branch of vacua.
