Quantum noncommutative ABJM theory: first steps
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2018
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Springer
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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 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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© The Authors. The work by C.P. Martin has been financially supported in part by the Spanish MINECO through grant FPA2014-54154-P. This work is also supported by the Croatian Science Foundation (HRZZ) under Contract No. IP-2014-09-9582, and we acknowledge the support of the COST Action MP1405 (QSPACE). J. You acknowledges support by the H2020 Twining project No. 692194, RBI-T-WINNING, and would like to acknowledge the support of W. Hollik and the Max-Planck-Institute for Physics, Munich, for hospitality. We also thank Johanna Erdmenger, Karl Landsteiner and Jun-bao Wu for many discussions on gauge/gravity duality and/or ABJM theory.