# Quantum K-Theory of Calabi-Yau Manifolds

## TL;DR

This paper explores the relationship between 3d N=2 supersymmetric gauge theories and quantum K-theory for Calabi-Yau manifolds, proposing a multi-cover formula linking BPS degeneracies to Gopakumar-Vafa invariants.

## Contribution

It introduces a multi-cover formula connecting quantum K-theoretic invariants with Gopakumar-Vafa invariants for Calabi-Yau manifolds with multiple Kähler moduli.

## Key findings

- Proposes a correspondence between 3d gauge theories and quantum K-theory.
- Develops a multi-cover formula relating BPS states to Gopakumar-Vafa invariants.
- Analyzes both global and local Calabi-Yau manifolds with several Kähler moduli.

## Abstract

The disk partition function of certain 3d N=2 supersymmetric gauge theories computes a quantum K-theoretic ring for Kahler manifolds X. We study the 3d gauge theory/quantum K-theory correspondence for global and local Calabi-Yau manifolds with several Kahler moduli. We propose a multi-cover formula that relates the 3d BPS world-volume degeneracies computed by quantum K-theory to Gopakumar-Vafa invariants.