K-theoretic quasimap invariants and their wall-crossing

Abstract

For each positive rational number $\epsilon$, we define $K$-theoretic $\epsilon$-stable quasimaps to certain GIT quotients $W\sslash G$. For $\epsilon >1$, this recovers the $K$-theoretic Gromov-Witten theory of $W\sslash G$ introduced in more general context by Givental and Y.-P. Lee. For arbitrary ${\epsilon }_1$ and ${\epsilon }_2$ in different stability chambers, these $K$-theoretic quasimap invariants are expected to be related by wall-crossing formulas. We prove wall-crossing formulas for genus zero $K$-theoretic quasimap theory when the target $W\sslash G$ admits a torus action with isolated fixed points and isolated one-dimensional orbits.

20 pages

References in corpus (1)

• The Hirzebruch--Riemann--Roch theorem in true genus-0 quantum K-theory

Cited by in corpus (3)

• Quantum $K$-theory of toric varieties, level structures, and 3d mirror symmetry
• Wall-Crossing in Genus Zero K-theoretic Landau-Ginzburg Theory
• $K$-theoretic quasimap wall-crossing