  We investigate a large class of $\mathcal{N} = (2, 2)$ supersymmetric field
theories in two dimensions, which contains the Murugan-Stanford-Witten model,
and can be naturally regarded as a disordered generalization of the
two-dimensional Landau-Ginzburg models. We analyze the two and four-point
functions of chiral superfields, and extract from them the central charge, the
operator spectrum, and the chaos exponent in these models. Some of the models
exhibit a conformal manifold parameterized by the variances of the random
couplings. We compute the Zamolodchikov metrics on the conformal manifold, and
demonstrate that the chaos exponent varies nontrivally along the conformal
manifolds. Finally, we introduce and perform some preliminary analysis of a
disordered generalization of the gauged linear sigma models, and discuss the
low energy theories as ensemble averages of Calabi-Yau sigma models over
complex structure moduli space.
