The exceptional Jordan algebra and the matrix string

TL;DR

This paper introduces a novel matrix model based on the exceptional Jordan algebra, which reproduces an octonionic compactification of matrix string theory with broken SO(8) symmetry, highlighting supersymmetry's relation to triality.

Contribution

It presents a new cubic matrix model rooted in the exceptional Jordan algebra that captures octonionic compactification features of matrix string theory.

Findings

Reproduces octonionic compactification at one loop

Identifies 27 matrix degrees of freedom with specific Spin(8) representations

Suggests supersymmetry is linked to triality of Spin(8) representations

Abstract

A new matrix model is described, based on the exceptional Jordan algebra. The action is cubic, as in matrix Chern-Simons theory. We describe a compactification that, we argue, reproduces, at the one loop level, an octonionic compactification of the matrix string theory in which SO(8) is broken to G2. There are 27 matrix degrees of freedom, which under Spin(8) transform as the vector, spinor and conjugate spinor, plus three singlets, which represent the two longitudinal coordinates plus an eleventh coordinate. Supersymmetry appears to be related to triality of the representations of Spin(8).