Categorical Primitive Forms and Gromov–Witten Invariants of An Singularities

Abstract

Abstract We introduce a categorical analogue of Saito’s notion of primitive forms. For the category $\textsf{MF}(\frac{1}{n+1}x^{n+1})$ of matrix factorizations of $\frac{1}{n+1}x^{n+1}$, we prove that there exists a unique, up to non-zero constant, categorical primitive form. The corresponding genus zero categorical Gromov–Witten invariants of $\textsf{MF}(\frac{1}{n+1}x^{n+1})$ are shown to match with the invariants defined through unfolding of singularities of $\frac{1}{n+1}x^{n+1}$.