Three-Algebra BFSS Matrix Theory

TL;DR

This paper extends the BFSS matrix theory using Lie 3-algebra, maintaining supersymmetry, and explores its dynamics revealing two distinct phases, one equivalent to the original model and another simpler supersymmetric phase.

Contribution

It introduces a Lie 3-algebra extension to the BFSS matrix theory and analyzes its phases, providing new insights into its structure and dynamics.

Findings

The extended model preserves supersymmetry.

Two distinct phases are identified in the minimal Lie 3-algebra model.

One phase reduces to the original matrix model, the other to a simpler supersymmetric model.

Abstract

We extend the BFSS matrix theory by means of Lie 3-algebra. The extended model possesses the same supersymmetry as the original BFSS matrix theory, and thus as the infinite momentum frame limit of M-theory. We study dynamics of the model by choosing the minimal Lie 3-algebra that includes u(N) algebra. We can solve a constraint in the minimal model and obtain two phases. In one phase, the model reduces to the original matrix model. In another phase, it reduces to a simple supersymmetric model.