Perturbative dynamics on fuzzy S2 and RP2
Abstract
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 beta-function for the O(N) theory on fuzzy RP2 at large N and show that in addition to the trivial one, it has a nontrivial fixed point that is accessible in perturbation theory.
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