Perturbative dynamics on fuzzy S^2 and RP^2

TL;DR

This paper explores scalar field theories on fuzzy spheres and real projective planes, revealing UV-IR mixing phenomena and identifying a nontrivial fixed point in the beta-function for theories on fuzzy RP^2.

Contribution

It constructs a renormalization scheme for fuzzy sphere theories, calculates the one-loop effective action, and demonstrates the absence of UV-IR mixing on fuzzy RP^2, including the beta-function analysis.

Findings

UV-IR mixing affects correlators on fuzzy S^2

Fuzzy RP^2 theories avoid UV-IR mixing

Nontrivial fixed point found in beta-function for fuzzy RP^2

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 RP^2 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 RP^2 at large N and show that in addition to the trivial one, it has a nontrivial fixed point that is accessible in perturbation theory.