Fuzzy torus in matrix model

We have calculated the free energy up to two loop to compare T2 with T4 in IIB matrix model. It turns out that T2 has smaller free energy than T4. We have also discussed the generation of the gauge group by considering k-coincident fuzzy tori and found that in this case U(1) gauge group is favored. This means that if the true vacuum is four-dimensional, it is not a simple fuzzy space considered here.