  We study some semi-infinite invariants associated to Landau-Ginzburg models.
These specialize classically to the usual twisted de Rham package and in the
case of vanishing potential to the chiral de Rham complex of Malikov,
Schechtman and Vaintrob, \cite{MSV}. Further we offer some small evidence that
these semi-infinite invariants can be associated to dg- categories more
generally, so that in the classical limit they reproduce the usual
non-commutative Hodge theory associated to the category.
