Stability of fuzzy S2×S2×S2 in IIB type matrix models

We study the stability of fuzzy S2×S2×S2 backgrounds in three different IIB type matrix models with respect to the change of the spins of each S2 at the two loop level. We find that S2×S2×S2 background is metastable and the effective action favors a single large S2 in comparison to the remaining S2×S2 in the models with Myers term. On the other hand, we find that a large S2×S2 in comparison to the remaining S2 is favored in IIB matrix model itself. We further study the stability of fuzzy S2×S2 background in detail in IIB matrix model with respect to the scale factors of each S2 as well. In this case, we find unstable directions which lower the effective action away from the most symmetric fuzzy S2×S2 background.