I will present recent and ongoing work with Tadashi Okazaki. We study certain configurations of M2-branes suspended between M5-branes, which are also related to interesting D3-brane and 5-branes configurations. Boundary conditions are imposed on the fields of the BLG or ABJM models, in order to preserve supersymmetry. In addition, the Chern-Simons action requires suitable boundary conditions for gauge invariance. With a topological twist there is a remarkable simplification -- all bosonic boundary conditions can be encoded in a condition on a complexified Chern-Simons gauge field. Naturally the result is a WZW model. Examining the fermionic fields we find that the model is in fact a supergroup WZW model. We then study a BPS index of this WZW model. For the case arising from BLG theory an explicit expression can be given in terms of a mock modular form. We discuss the modular completion of the index, at the cost of a holomorphic anomaly. It may also be possible to describe supergroup WZW models using a quantum mechanics model, as has been done recently for unitary groups.