Eur. Phys. J. C (2016) 76: 180
https://doi.org/10.1140/epjc/s10052-016-4022-z

Regular Article - Theoretical Physics

Renormalization on noncommutative torus

¹ Instituto de Física La Plata-CONICET, Universidad Nacional de La Plata, C.C. 67 (1900), La Plata, Argentina
² CMCC, Universidade Federal do ABC, Santo André, SP, CEP 09210-180, Brazil
³ Department of Physics, Tomsk State University, Tomsk, Russia

^* e-mail: dvassil@gmail.com

Received: 13 February 2016
Accepted: 14 March 2016
Published online: 1 April 2016

Abstract

We study a self-interacting scalar theory on the d-dimensional noncommutative torus. We determine, for the particular cases and , 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 .