Fuzzy Torus in Matrix Model

TL;DR

This paper compares free energies of fuzzy tori in the IIB matrix model, finding T^2 is energetically favored over T^4, and discusses gauge group generation, suggesting the true vacuum may not be a simple fuzzy space.

Contribution

It calculates the free energy up to two loops for fuzzy tori in the IIB matrix model and analyzes gauge group generation, providing insights into the favored vacuum structure.

Findings

T^2 has smaller free energy than T^4 in the model.

U(1) gauge group is favored in k-coincident fuzzy tori.

The true vacuum may not be a simple fuzzy space.

Abstract

We have calculated the free energy up to two loop to compare T^2 with T^4 in IIB matrix model. It turns out that T^2 has smaller free energy than T^4. 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.