Stability of Fuzzy S^2 x S^2 x S^2 in IIB Type Matrix Models

TL;DR

This paper investigates the stability of fuzzy S^2 x S^2 x S^2 backgrounds in IIB matrix models, revealing metastability and favored configurations depending on model specifics and scale factors.

Contribution

It provides a detailed two-loop analysis of the stability of fuzzy S^2 x S^2 x S^2 backgrounds in various IIB matrix models, highlighting conditions for metastability and preferred configurations.

Findings

Fuzzy S^2 x S^2 x S^2 is metastable in these models.

A single large S^2 is favored over S^2 x S^2 in models with Myers term.

Large S^2 x S^2 is favored in the IIB matrix model itself.

Abstract

We study the stability of fuzzy S^2 x S^2 x S^2 backgrounds in three different IIB type matrix models with respect to the change of the spins of each S^2 at the two loop level. We find that S^2 x S^2 x S^2 background is metastable and the effective action favors a single large S^2 in comparison to the remaining S^2 x S^2 in the models with Myers term. On the other hand, we find that a large S^2 x S^2 in comparison to the remaining S^2 is favored in IIB matrix model itself. We further study the stability of fuzzy S^2 x S^2 background in detail in IIB matrix model with respect to the scale factors of each S^2 as well. In this case, we find unstable directions which lower the effective action away from the most symmetric fuzzy S^2 x S^2 background.