Quantum noncommutative ABJM theory: first steps

TL;DR

This paper introduces a noncommutative version of ABJM quantum field theory, demonstrating its supersymmetry, UV finiteness at one-loop, and smooth commutative limits, suggesting stability against IR instabilities.

Contribution

It is the first formulation of ABJM theory on noncommutative spacetime with explicit one-loop calculations showing UV finiteness and supersymmetry preservation.

Findings

One-loop 1PI functions are UV finite.

The theory has a smooth limit as noncommutativity vanishes.

No noncommutative IR instabilities observed.

Abstract

We introduce ABJM quantum field theory in the noncommutative spacetime by using the component formalism and show that it is N=6 supersymmetric. For the U(1)_{\kappa} x U(1)_{-\kappa} case, we compute all one-loop 1PI two and three point functions in the Landau gauge and show that they are UV finite and have well-defined commutative limits theta^{\mu\nu} -> 0, corresponding exactly to the 1PI functions of the ordinary ABJM field theory. This result also holds for all one-loop functions which are UV finite by power counting. It seems that the quantum noncommutative ABJM field theory is free from the noncommutative IR instabilities.