Renormalization on noncommutative torus

Original · EN

We study a self-interacting scalar φ⁴ 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.