Topic: Towards a Mathematical Definition of 5D Wilson Loops

Speaker: Dr. Xin Wang

Coordinates: PCFT C1124, 16:00, Tuesday November 21

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 topological strings on the same manifold X. These calculations are related to the Gromov-Witten invariants in the mathematical literature. While the BPS states of a half-BPS Wilson loop operator in the 5D gauge theory have been discussed in recent physics literature, the mathematical definition is still missing. In this presentation, based on collaborations with Guo Shuai and Longting Wu, I will give a mathematical rigorous definition of the 5D Wilson loop in terms with Gromov-Witten invariants, and its physical origin from M-theory.