Theoretical Physics Seminar: Xin Wang

Title: 5D Wilson Loops and Topological Strings

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 of the Calabi-Yau threefold X, which 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, which is a charged object under the one-form symmetry. Based on M-theory realization, we derive the BPS expansion of the expectation value of the Wilson loop operator in terms of BPS sectors. It turns out that the BPS sectors can be realized and computed from topological string theories. In the unrefined limit, the BPS sectors serve as generating functions for Gromov-Witten invariants on compact (semi)-Fano threefolds constructed from X. We further conjecture the refined holomorphic anomaly equations for the VEVs of the Wilson loop operators. These equations can be used to completely solve the refined BPS invariants of Wilson loops for local \mathbb{P}^2 and local \mathbb{P}^1\times \mathbb{P}^1 completely.