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

Abstract

We demonstrate that the UV/IR mixing problems found recently for a scalar $ϕ^4$ 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 $ϕ^4$ vertex. In the limit of the commutative sphere, the perturbation theory of this modified action matches that of the commutative theory.