In this talk, I will discuss the correspondence between 3d gauge theory and quantum K-theory. This is a 3d uplift of the well-known relation between 2d gauged linear sigma models (GLSMs) with target variety X (a.k.a the Higgs branch) and the quantum cohomology of X. One way to state this correspondence is the following: half-BPS line operators (e.g. Wilson lines) are in one-to-one correspondence with coherent sheaves (e.g. vector bundles) on the Higgs branch. In this talk, after reviewing these correspondences in general, I will focus on the case where X is a partial flag manifold. For a special choice of basis of the K-theory ring of X, I will show how one can construct the corresponding set of half-BPS line operators on the gauge theory side. I will also show how, using earlier results from supersymmetric localization, one can work out the explicit relations of the quantum K-theory ring of the partial flag manifold. This is based on work with Wei Gu, Cyril Closset, Eric Sharpe, Hao Zhang, and Hao Zou..

https://indico.math.cnrs.fr/event/15155/