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Theoretical Physics
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) 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 ordinar
y ABJM field theory. This result also holds for all one-loop functions which are U V finite by power counting. It seems that the quantum noncommutative ABJM field theory is free from the noncommutative IR instabilities.
