  The theory of Mixed-Spin-P (MSP) fields was introduced by Chang-Li-Li-Liu for
the quintic threefold, aiming at studying its higher-genus Gromov-Witten
invariants. Chang-Guo-Li has successfully applied it to prove conjectures on
the higher-genus Gromov-Witten invariants, including the BCOV Feynman rule and
Yamaguchi-Yau's polynomiality conjecture. This paper generalizes the MSP fields
construction to more general GIT quotients, including global complete
intersection Calabi-Yau manifolds in toric varieties. This hopefully provides a
geometric platform to effectively compute higher-genus Gromov-Witten invariants
for complete intersections in toric varieties. The key to our paper is a
stability condition which guarantees the separatedness and properness of the
cosection degeneracy locus in the moduli. It also gives a mathematical
definitions for more general Landau-Ginzburg theories.
