The M2-M5 brane system and a generalized Nahm's equation

We propose an equation that describes M2-branes ending on M5-branes, and which generalizes the description of the D1-D3 system via Nahm's equation. The simplest solution to this equation constructs the transverse geometry in terms of a fuzzy three sphere. We show that the solution passes a number of consistency checks including a calculation of the energy of the system, matching to the self-dual string solution in the M5-brane worldvolume, and a study of simple fluctuations about the ground state configuration. We write down certain terms in the effective action of multiple membranes, which includes a sextic scalar coupling.