Singular BPS boundary conditions in $\mathcal{N} = (2,2)$ supersymmetric gauge theories

We derive general BPS boundary conditions in two-dimensional $\mathcal{N}=(2,2)$ supersymmetric gauge theories. We analyze the solutions of these boundary conditions, and in particular those that allow the bulk fields to have poles at the boundary. We also present the brane configurations for the half- and quarter-BPS boundary conditions of the $\mathcal{N}=(2,2)$ supersymmetric gauge theories in terms of branes in Type IIA string theory. We find that both A-type and B-type brane configurations are lifted to M-theory as a system of M2-branes ending on an M5-brane wrapped on a product of a holomorphic curve in $\mathbb{C}^2$ with a special Lagrangian 3-cycle in $\mathbb{C}^3$.