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

TL;DR

This paper demonstrates that one-loop four- and six-point functions in quantum noncommutative ABJM theory are UV finite, well-behaved in the commutative limit, and free from UV/IR instabilities, indicating a smooth transition to the ordinary ABJM theory.

Contribution

It provides the first detailed analysis of higher-point functions in noncommutative ABJM theory, establishing their finiteness and stability at one-loop order.

Findings

One-loop four- and six-point functions are UV finite.

The functions have a well-defined limit as noncommutativity vanishes.

The theory is free from UV and IR instabilities at one-loop.

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 $(\theta^{\mu\nu}\rightarrow 0)$ 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 $\theta^{\mu\nu}\rightarrow 0$ it flows to the ordinary ABJM theory.