Differential Geometry Seminar | 5D Wilson Loops and Topological Strings on Fano-threefolds

Abstract

Geometric engineering provides a rich class of 5D supersymmetric gauge theories with eight supercharges, arising from M-theory compactification on non-compact Calabi-Yau threefolds. The counting of BPS states in the low-energy gauge theory is determined by the degeneracies of M2-branes wrapping holomorphic two-cycles in the Calabi-Yau threefold X. These degeneracies can also be calculated from the (refined) topological strings on the same manifold X.

In this talk, I will explore the BPS spectrum of the 5D gauge theory with the insertion of a half-BPS Wilson loop operator. Utilizing M-theory realization, we derive the BPS expansion of the expectation value of the Wilson loop operator in terms of BPS sectors. It is found that the BPS sectors can be realized and computed from topological string theories. In the unrefined limit, the BPS sectors act as generating functions for Gromov-Witten invariants on compact (semi)-Fano threefolds constructed from X.

We further conjecture a new refined holomorphic anomaly equations for the generating functions of the Wilson loops. These equations can completely solve the refined BPS invariants of Wilson loops for local \mathbb{P}^2 and local \mathbb{P}^1\times\mathbb{P}^1.

Speaker

I am interested in string theory, SUSY gauge theory, and their geometries. I am studying blowup equations for 6d/5d SCFTs, little string theories, and quantum spectral curves for them.

I'm currently a Research Fellow at the Korea Institute for Advanced Study. I was a Postdoctoral Fellow at MPIM during 2018-2020; my mentor was Prof. Albrecht Klemm. I received my Ph.D. in Theoretical Physics from the University of Science and Technology of China in 2018. My advisor was Prof. Min-xin Huang.