Wall-crossing in genus-zero hybrid theory

Abstract

The hybrid model is the Landau-Ginszburg-type theory that is expected, via the Landau-Ginzburg/Calabi-Yau correspondence, to match the Gromov-Witten theory of a complete intersection in weighted projective space. We prove a wall-crossing formula exhibiting the dependence of the genus-zero hybrid model on its stability parameter, generalizing the work of the second author and Ruan for quantum singularity theory and paralleling the work of Ciocan-Fontanine--Kim for quasimaps. This completes the proof of the genus-zero Landau-Ginzburg/Calabi-Yau correspondence for complete intersections of hypersurfaces of the same degree, as well as the proof of the all-genus hybrid wall-crossing theorem, which is work of the first author, Janda, and Ruan.