Renormalization on noncommutative torus

DASCANIO, D.; VASSILEVICH, D.V.; PISANI, P.

EUROPEAN PHYSICAL JOURNAL C - PARTICLES AND FIELDS

SPRINGER

Año: 2016 vol. 76 p. 180 - 190

1434-6044

We study a self-interacting scalar \phi4 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 ultraviolet/infrared 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 \theta.