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#### Quantum noncommutative ABJM theory: first steps

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##### Citation

Martin, C. P., Trampetic, J., & You, J. (2018). Quantum noncommutative ABJM theory:
first steps.* Journal of High Energy Physics,* (1804), 070. Retrieved from https://publications.mppmu.mpg.de/?action=search&mpi=MPP-2017-282.

Cite as: https://hdl.handle.net/21.11116/0000-0003-F84F-E

##### 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.