Matrix models on the fuzzy sphere

Abstract

Field theory on a fuzzy noncommutative sphere can be considered as a particular matrix approximation of field theory on the standard commutative sphere. We investigate from this point of view the scalar ${\varphi }^4$ theory. We demonstrate that the UV/IR mixing problems of this theory are localized to the tadpole diagrams and can be removed by an appropiate (fuzzy) normal ordering of the ${\varphi }^4$ vertex. The perturbative expansion of this theory reduces in the commutative limit to that on the commutative sphere.

6 pages, LaTeX2e, Talk given at the NATO Advanced Research Workshop on Confiment, Topology, and other Non-Perturbative Aspects of QCD, Stara Lesna, Slovakia, Jan. 21-27, 2002