  In this paper, we study a class of heterotic Landau-Ginzburg models. We show
that the action can be written as a sum of BRST-exact and non-exact terms. The
non-exact terms involve the pullback of the complexified Kahler form to the
worldsheet and terms arising from the superpotential, which is a Grassmann-odd
holomorphic function of the superfields. We then demonstrate that the action is
invariant on-shell under supersymmetry transformations up to a total
derivative. Finally, we extend the analysis to the case in which the
superpotential is not holomorphic. In this case, we find that supersymmetry
imposes a constraint which relates the nonholomorphic parameters of the
superpotential to the Hermitian curvature. Various special cases of this
constraint have previously been used to establish properties of Mathai-Quillen
form analogues which arise in the corresponding heterotic Landau-Ginzburg
models. There, it was claimed that supersymmetry imposes those constraints. Our
goal in this paper is to support that claim. The analysis for the
nonholomorphic case also reveals a constraint imposed by supersymmetry that we
did not anticipate from studies of Mathai-Quillen form analogues.
