Matrix ${\varphi }^4$ Models on the Fuzzy Sphere and their Continuum Limits

Abstract

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

19 pages of LaTeX, with 3 figures

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• Scaling Limits of the Fuzzy Sphere at one Loop
• Fuzzy CP2
• Gauge-fixing independence of IR divergences in non-commutative U(1), perturbative tachyonic instabilities and supersymmetry
• Wilsonian Renormalization Group and the Non-Commutative IR/UV Connection
• Perturbative dynamics on fuzzy S^2 and RP^2
• Instability of Non-Commutative SYM Theories at Finite Temperature
• Hard Non-commutative Loops Resummation
• UV/IR connection, a matrix perspective

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