Quantum noncommutative ABJM theory: first steps

Abstract

Abstract We introduce ABJM quantum field theory in the noncommutative spacetime by using the component formalism and show that it is $$ \mathcal{N} $$ N = 6 supersymmetric. For the U(1) κ × U(1)−κ 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 θ μν → 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 noncommutative quantum ABJM field theory is free from the noncommutative IR instabilities.