Four-algebraic extension of the IIB matrix model

TL;DR

This paper introduces a four-algebraic extension of the IIB matrix model using Lie 4-algebras, which preserves supersymmetry and reveals three distinct phases, including reductions to known models and a torus dynamics model.

Contribution

It constructs a novel four-algebraic extension of the IIB matrix model based on Lie 4-algebras, maintaining supersymmetry and analyzing its phase structure.

Findings

The model has three phases with different reductions.

In the first phase, it reduces to the original IIB matrix model.

In the third phase, it describes the dynamics of matrices representing a torus.

Abstract

We make a four-algebraic extension of the IIB matrix model. The extension can be made by any Lie 4-algebra. The four-algebraic model has the same supersymmetry as the IIB matrix model, and hence as type IIB superstring theory. The four-algebraic model contains twelve bosonic matrices; two of these will be identified with two extra dimensions that characterize F-theory. We construct a Lie 4-algebra that incorporates $u(N)$ Lie algebra and analyze the model explicitly by choosing it. We have three phases in the model with that specific algebra. In the first phase, it reduces to the original IIB matrix model. In the second phase, it reduces to a simple supersymmetric model. In the third phase, it reduces to a model that describes only the dynamics of the two matrices representing the torus.