Duality and Light Cone Symmetries of the Equations of Motion

TL;DR

This paper explores the symmetries of equations of motion in matrix theory for M theory on a torus, revealing how S duality manifests as a Nahm-type transformation and a 9-11 flip.

Contribution

It identifies light cone coordinate rescaling symmetries and connects S duality to a Nahm-type transformation within the matrix theory framework.

Findings

Symmetries correspond to rescaling of light cone coordinates.

S duality is realized as a Nahm-type transformation.

A 9-11 flip relates different descriptions of M theory.

Abstract

The matrix theory description of the discrete light cone quantization of $M$ theory on a $T^{2}$ is studied. In terms of its super Yang- Mills description, we identify symmetries of the equations of motion corresponding to independent rescalings of one of the world sheet light cone coordinates, which show how the $S$ duality of Type IIB string theory is realized as a Nahm-type transformation. In the $M$ theory description this corresponds to a simple $9-11$ flip.