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)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

θμν → 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.

# Quantum noncommutative ABJM theory: first steps

2018, April 12

JHEP