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We define a generalization of Fan-Jarvis-Ruan-Witten theory, a "hybrid" modelassociated to a collection of quasihomogeneous polynomials of the same weightsand degree, which is expected to match the Gromov-Witten theory of theCalabi-Yau complete intersection cut out by the polynomials. In genus zero, weprove that the correspondence holds for any such complete intersection ofdimension three in ordinary, rather than weighted, projective space. Theseresults generalize those of Chiodo-Ruan for the quintic threefold, and as inthat setting, Givental's quantization can be used to yield a conjecturalrelation between the full higher-genus theories.

Landau-Ginzburg/Calabi-Yau correspondence for the complete intersections X_{3,3} and X_{2,2,2,2}