Extension of IIB Matrix Model by Three-Algebra

TL;DR

This paper extends the IIB matrix model using Lie 3-algebra, maintaining supersymmetry, and explores its dynamics, revealing two classical phases with different reductions of the action.

Contribution

It introduces a Lie 3-algebra extension of the IIB matrix model that preserves supersymmetry and analyzes its classical phases using a minimal Lie 3-algebra.

Findings

The extended model admits any Lie 3-algebra with supersymmetry.

Two classical phases are identified in the minimal Lie 3-algebra case.

One phase reduces to the original IIB matrix model, the other to a simpler, more analyzable action.

Abstract

We construct a Lie 3-algebra extended model of the IIB matrix model. It admits any Lie 3-algebra and possesses the same supersymmetry as the original matrix model, and thus as type IIB superstring theory. We examine dynamics of the model by taking minimal Lie 3-algebra that includes u(N) Lie algebra as an example. There are two phases in the minimally extended model at least classically. The extended action reduces to that of the IIB matrix model in one phase. In other phase, it reduces to a more simple action, which is rather easy to analyze.