Quantum noncommutative ABJM theory: first steps

2018, April 12
Carmelo P. Martin, Josip Trampetic and Jiangyang Youd

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.