Fuzzy Spacetime with SU(3) Isometry in IIB Matrix Model

TL;DR

This paper investigates fuzzy spacetimes with SU(3) symmetry within the IIB matrix model, analyzing their effective actions at two loops and revealing dimensional scaling behaviors and stability preferences.

Contribution

It introduces a class of fuzzy spacetimes with SU(3) isometry in the IIB matrix model and studies their two-loop effective actions across different dimensions.

Findings

Effective action scales as N on 4D manifolds and as N^{4/3} on 6D manifolds.

The 4D CP2 spacetime has the smallest effective action, indicating stability.

Spacetime dimensionality influences the effective action scaling in the model.

Abstract

A group of fuzzy spacetime with SU(3) isometry is studied at the two loop level in IIB matrix model. It consists of spacetime from 4 to 6 dimensions, namely from CP2 to SU(3)/U(1)x U(1). The effective action scales in a universal manner in the large N limit as N and N^{4/3} on 4 and 6 dimensional manifolds respectively. The 4 dimensional spacetime CP2 possesses the smallest effective action in this class.