Matrix ϕ⁴ Models on the Fuzzy Sphere and their Continuum Limits

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We demonstrate that the UV/IR mixing problems found recently for a scalar ϕ⁴ 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 ϕ⁴ vertex. In the limit of the commutative sphere, the perturbation theory of this modified action matches that of the commutative theory.