Gepner type stability conditions on graded matrix factorizations

We introduce the notion of Gepner type Bridgeland stability conditions on triangulated categories, which depends on a choice of an autoequivalence and a complex number. We conjecture the existence of Gepner type stability conditions on the triangulated categories of graded matrix factorizations of weighted homogeneous polynomials. Such a stability condition may give a natural stability condition for Landau-Ginzburg B-branes, and correspond to the Gepner point of the stringy Kahler moduli space of a quintic 3-fold. The main result is to show our conjecture when the variety defined by the weighted homogeneous polynomial is a complete intersection of hyperplanes in a Calabi-Yau manifold with dimension less than or equal to two.