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arXiv · 1602.01479

Renormalization on noncommutative torus

D. D'Ascanio·P. Pisani·D. V. Vassilevich
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Abstract

We study a self-interacting scalar $φ^4$ theory on the $d$-dimensional noncommutative torus. We determine, for the particular cases $d=2$ and $d=4$, the counterterms required by one-loop renormalization. We discuss higher loops in two dimensions and two-loop contributions to the self-energy in four dimensions. Our analysis points toward the absence of any problems related to the UV/IR mixing and thus to renormalizability of the theory. However, we find another potentially troubling phenomenon which is a wild behavior of the two-point amplitude as a function of the noncommutativity matrix $θ$.

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D. D'Ascanio, P. Pisani, D. V. Vassilevich. 2016-04-06. Renormalization on noncommutative torus. https://doi.org/10.1140/epjc%2Fs10052-016-4022-z

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