Topological M-Strings and Supergroup WZW Models

We study the boundary conditions in the topologically twisted Chern-Simons matter theories with the Lie 3-algebraic structure. We find that the supersymmetric boundary conditions and the gauge invariant boundary conditions can be unified as the complexified gauge invariant boundary conditions which lead to the supergroup WZW models. We propose that the low-energy effective field theories on the two-dimensional intersection of multiple M2-branes on a holomorphic curve inside K3 with two non-parallel M5-branes on the K3 are supergroup WZW models from the topologically twisted BLG-model and the ABJM-model.