We analyze the expectation value of observables in a scalar theory on the fuzzy two-sphere, represented as a generalized Hermitian matrix model. We calculate explicitly the form of the expectation values in the large-$N$ limit and demonstrate that, for any single kind of field (matrix), the distribution of its eigenvalues is still a Wigner semicircle but with a renormalized radius. For observables involving more than one type of matrix, we obtain a new distribution corresponding to correlated Wigner semicircles.

• Received 28 September 2011

DOI:https://doi.org/10.1103/PhysRevD.85.045021