The (2,0) Superalgebra, Null M-branes and Hitchin's System

We present an interacting system of equations with sixteen supersymmetries and an $SO(2)\times SO(6)$ R-symmetry where the fields depend on two space and one null dimensions that is derived from a representation of the six-dimensional (2,0) superalgebra. The system can be viewed as two M5-branes compactified on $S_{-}^1\times {\mathbb{T}}^2$ or equivalently as M2-branes on ${\mathbb{R}}_{+}\times {\mathbb{R}}^2$, where $\pm$ refer to null directions. We show that for a particular choice of fields the dynamics can be reduced to motion on the moduli space of solutions to the Hitchin system. We argue that this provides a description of intersecting null M2-branes and is also related by U-duality to a DLCQ description of four-dimensional maximally supersymmetric Yang-Mills.