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- W3122231953 abstract "A bstract We consider the noncommutative space $ mathbb{R}_{lambda}^3 $ , a deformation of the algebra of functions on $ {{mathbb{R}}^3} $ which yields a “foliation” of $ {{mathbb{R}}^3} $ into fuzzy spheres. We first construct a natural matrix base adapted to $ mathbb{R}_{lambda}^3 $ . We then apply this general framework to the one-loop study of a two-parameter family of real-valued scalar noncommutative field theories with quartic polynomial interaction, which becomes a non-local matrix model when expressed in the above matrix base. The kinetic operator involves a part related to dynamics on the fuzzy sphere supplemented by a term reproducing radial dynamics. We then compute the planar and non-planar 1-loop contributions to the 2-point correlation function. We find that these diagrams are both finite in the matrix base. We find no singularity of IR type, which signals very likely the absence of UV/IR mixing. We also consider the case of a kinetic operator with only the radial part. We find that the resulting theory is finite to all orders in perturbation expansion." @default.
- W3122231953 created "2021-02-01" @default.
- W3122231953 creator A5012995360 @default.
- W3122231953 creator A5050882080 @default.
- W3122231953 date "2013-04-01" @default.
- W3122231953 modified "2023-10-03" @default.
- W3122231953 title "Noncommutative field theories on $ mathbb{R}_{lambda}^3 $: towards UV/IR mixing freedom" @default.
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- W3122231953 doi "https://doi.org/10.1007/jhep04(2013)115" @default.
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