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.