  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. These
results generalize those of Chiodo-Ruan for the quintic threefold, and as in
that setting, Givental's quantization can be used to yield a conjectural
relation between the full higher-genus theories.
