Quantum noncommutative ABJM field theory: four- and six-point functions

Abstract

Following our previous paper Quantum noncommutative ABJM theory: first steps, JHEP {\bf 1804} (2018) 070), in this article we investigate one-loop 1PI four-, and six-point functions by using the component formalism in the Landau gauge and show that they are UV finite and have well-defined $(\hat{I}{¸}^{\hat{I}¼\hat{I}½}\to 0)$ limit. Those results also hold for all one-loop functions which are UV finite by power counting. In summary, taking into account results from previous paper, JHEP {\bf 1804} (2018) 070), and this paper, we conclude that, at least at one-loop order, the NCABJM theory is free from the noncommutative UV and IR instabilities, and that in the limit $\hat{I}{¸}^{\hat{I}¼\hat{I}½}\to 0$ it flows to the ordinary ABJM theory.

78 pages, 16 figures. Version just published in JHEP