Perturbative dynamics on the fuzzy S2 and RP2

By considering scalar theories on the fuzzy sphere as matrix models, we construct a renormalization scheme and calculate the one-loop effective action. Because of UV–IR mixing, the two- and the four-point correlators at low energy are not slowly varying functions of external momenta. Interestingly, we also find that field theories on fuzzy RP2 avoid UV–IR mixing and hence are much more like conventional field theories. We calculate the one-loop β-function for the O(N) theory on fuzzy RP2 at large N and show there exists a nontrivial fixed point that is accessible in perturbation theory.