Extension of IIB Matrix Model by Three-Algebra

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.