E6 Matrix Model

TL;DR

This paper introduces a novel matrix model based on the exceptional Lie group E6, deriving a matrix Chern-Simons theory and exploring its properties and potential cosmological implications.

Contribution

It constructs a new E6-based matrix model with doubled degrees of freedom and derives a related matrix Chern-Simons theory, extending previous models like Smolin's.

Findings

Model has twice as many degrees of freedom as Smolin's.

Properties of the product space resemble those of the physical Hilbert space.

Potential for introducing cosmological terms via compactification.

Abstract

We consider a new matrix model based on the simply connected compact exceptional Lie group E6. A matrix Chern-Simons theory is directly derived from the invariant on E6. It is stated that the similar argument as Smolin which derives an effective action of the matrix string type can also be held in our model. An important difference is that our model has twice as many degrees of freedom as Smolin's model has. One way to introduce the cosmological term is the compactification on directions. It is of great interest that the properties of the product space $\Vec{\mathfrak{J}^c} \times \Vec{\mathcal{G}}$, in which the degrees of freedom of our model live, are very similar to those of the physical Hilbert space.