Abstract

The refined Gopakumar-Vafa numbers of a Calabi-Yau 3-fold were originally introduced as an intermediate step towards defining the Gopakumar-Vafa invariants. From the M-theory perspective, they count the BPS states of M2 branes wrapping holomorphic 2-cycles. If the Calabi-Yau 3-fold is non-compact, the refined Gopakumar-Vafa numbers are invariants that can be defined from 5D gauge theory on the Omega-background. If the Calabi-Yau 3-fold is an elliptic-fibered compact 3-fold, we argue that the BPS numbers can be related to the BPS states of Wilson loop operators in the 5d gauge theory, which can be refined. We also propose a novel refined holomorphic anomaly equation for compact elliptic-fibered Calabi-Yau 3-folds.

报告人简介

王昕，本科、硕⼠、博⼠毕业于中国科学技术⼤学近代物理系。先后在德国⻢克斯-普朗克数学研究所、韩国⾼等科学院进⾏博⼠后研究⼯作。研究⽅向是拓扑弦理论，五维、六维超对称场论及其相关的数学。