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

## TL;DR

This paper introduces a new supersymmetric system derived from the (2,0) superalgebra that describes intersecting null M2-branes and relates to Hitchin's system and 4D super Yang-Mills via U-duality.

## Contribution

It presents a novel interacting system with 16 supersymmetries based on the (2,0) superalgebra, connecting M-branes, Hitchin's system, and U-duality.

## Key findings

- System describes intersecting null M2-branes.
- Reduces to Hitchin's moduli space dynamics.
- Links to 4D maximally supersymmetric Yang-Mills.

## Abstract

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.