Matrix $\phi^4$ Models on the Fuzzy Sphere and their Continuum Limits

TL;DR

This paper addresses UV/IR mixing issues in scalar 4 theory on the fuzzy sphere by modifying the action through normal ordering, ensuring the continuum limit aligns with the commutative theory.

Contribution

It introduces a modification to the 4 action on the fuzzy sphere that resolves UV/IR mixing by localizing it to tadpole diagrams, aligning the theory with the commutative case.

Findings

UV/IR mixing is localized to tadpole diagrams

Modified action via normal ordering resolves mixing issues

Perturbation theory matches the commutative limit

Abstract

We demonstrate that the UV/IR mixing problems found recently for a scalar $\phi^4$ theory on the fuzzy sphere are localized to tadpole diagrams and can be overcome by a suitable modification of the action. This modification is equivalent to normal ordering the $\phi^4$ vertex. In the limit of the commutative sphere, the perturbation theory of this modified action matches that of the commutative theory.