Wall-crossing in genus-zero hybrid theory

TL;DR

This paper establishes a wall-crossing formula for genus-zero hybrid models, demonstrating how these models depend on stability parameters and confirming the Landau-Ginzburg/Calabi-Yau correspondence for certain complete intersections.

Contribution

It generalizes previous work to prove a comprehensive wall-crossing formula for genus-zero hybrid models, completing the Landau-Ginzburg/Calabi-Yau correspondence for specific hypersurface complete intersections.

Findings

Proved a genus-zero hybrid wall-crossing formula.

Confirmed the Landau-Ginzburg/Calabi-Yau correspondence for hypersurfaces.

Established the all-genus hybrid wall-crossing theorem.

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.