K-theoretic Gromov--Witten invariants in genus 0 and integrable hierarchies

TL;DR

This paper demonstrates that genus-0 K-theoretic Gromov--Witten invariants are controlled by an integrable hydrodynamic hierarchy, and establishes the hierarchy's completeness under semisimplicity conditions.

Contribution

It establishes a connection between genus-0 K-theoretic Gromov--Witten invariants and integrable hierarchies, extending understanding of their structure and solvability.

Findings

Genus-0 invariants are governed by an integrable hierarchy.

Completeness of the hierarchy is proven under semisimplicity.

Provides a new framework linking K-theoretic invariants and integrable systems.

Abstract

We prove that the genus-0 invariants in K-theoretic Gromov--Witten theory are governed by an integrable hierarchy of hydrodynamic type. If the K-theoretic quantum product is semisimple, then we also prove the completeness of the hierarchy.