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Quantum noncommutative ABJM theory: first steps

A preprint version of the article is available at arXiv.

Abstract

We introduce ABJM quantum field theory in the noncommutative spacetime by using the component formalism and show that it is \( \mathcal{N} \) = 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.

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Correspondence to Josip Trampetic.

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ArXiv ePrint: 1711.09664

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Martin, C.P., Trampetic, J. & You, J. Quantum noncommutative ABJM theory: first steps. J. High Energ. Phys. 2018, 70 (2018). https://doi.org/10.1007/JHEP04(2018)070

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Keywords

  • Chern-Simons Theories
  • Non-Commutative Geometry