Wall-Crossing in Genus Zero K-theoretic Landau-Ginzburg Theory

TL;DR

This paper investigates K-theoretic quantum invariants in genus zero Landau-Ginzburg theory, establishing a wall-crossing formula by linking generating functions to the Lagrangian cone of permutation-equivariant K-theoretic FJRW theory.

Contribution

It introduces a new wall-crossing formula for K-theoretic invariants in genus zero Landau-Ginzburg theory, connecting generating functions to the Lagrangian cone.

Findings

Proves a wall-crossing formula for K-theoretic invariants.

Shows generating functions lie on the Lagrangian cone of the theory.

Establishes a connection between invariants and permutation-equivariant K-theoretic FJRW theory.

Abstract

For a Fermat quasi-homogeneous polynomial $W$, we study a family of K-theoretic quantum invariants parametrized by a positive rational number $\epsilon$. We prove a wall-crossing formula by showing the generating functions lie on the Lagrangian cone of the permutation-equivariant K-theoretic FJRW theory of $W$.