  In the previous study, we formulate a matrix model renormalization group
based on the fuzzy spherical harmonics with which a notion of high/low energy
can be attributed to matrix elements, and show that it exhibits locality and
various similarity to the usual Wilsonian renormalization group of quantum
field theory. In this work, we continue the renormalization group analysis of a
matrix model with emphasis on nonlocal interactions where the fields on
antipodal points are coupled. They are indeed generated in the renormalization
group procedure and are tightly related to the noncommutative nature of the
geometry. We aim at formulating renormalization group equations including such
nonlocal interactions and finding existence of nontrivial field theory with
antipodal interactions on the fuzzy sphere. We find several nontrivial fixed
points and calculate the scaling dimensions associated with them. We also
consider the noncommutative plane limit and then no consistent fixed point is
found. This contrast between the fuzzy sphere limit and the noncommutative
plane limit would be manifestation in our formalism of the claim given by Chu,
Madore and Steinacker that the former does not have UV/IR mixing, while the
latter does.
