The Landau-Ginzburg/Calabi-Yau Correspondence for Certain Complete Intersections.

Abstract

We define a generalization of Fan-Jarvis-Ruan-Witten theory, a "hybrid" model associated to a collection of quasihomogeneous polynomials of the same weights and degree, which is expected to match the Gromov-Witten theory of the Calabi-Yau complete intersection cut out by the polynomials. In genus zero, we prove that the correspondence holds for any such complete intersection of dimension three in ordinary, rather than weighted, projective space, generalizing the results of Chiodo-Ruan for the quintic threefold.