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Monopoles, three-algebras and ABJM theories with \( \mathcal{N} = 5,6,8 \) supersymmetry

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Abstract

We extend the hermitian three-algebra formulation of ABJM theory to include U(1) factors. With attention payed to extra U(1) factors, we refine the classification of \( \mathcal{N} = 6 \) ABJM theories. We argue that essentially the only allowed gauge groups are SU(N) × SU(N), U(N) × U(M) and Sp(N) × U(1) and that we have only one independent Chern-Simons level in all these cases. Our argument is based on integrality of the U(1) Chern-Simons levels and supersymmetry. A relation between monopole operators and Wilson lines in Chern-Simons theory suggests certain gauge representations of the monopole operators. From this we classify cases where we can not expect enhanced \( \mathcal{N} = 8 \) supersymmetry. We also show that there are two equivalent formulations of \( \mathcal{N} = 5 \) ABJM theories, based on hermitian three-algebra and quaternionic three-algebra respectively. We suggest properties of monopoles in \( \mathcal{N} = 5 \) theories and show how these monopoles may enhance supersymmetry from \( \mathcal{N} = 5 \) to \( \mathcal{N} = 6 \).

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Authors and Affiliations

  1. Center for quantum spacetime (CQUeST), Sogang University, Seoul, 121-742, Korea

    Andreas Gustavsson

  2. School of Physics & Astronomy, Seoul National University, Seoul, 151-747, Korea

    Andreas Gustavsson

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  1. Andreas Gustavsson
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Correspondence to Andreas Gustavsson.

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Gustavsson, A. Monopoles, three-algebras and ABJM theories with \( \mathcal{N} = 5,6,8 \) supersymmetry. J. High Energ. Phys. 2011, 37 (2011). https://doi.org/10.1007/JHEP01(2011)037

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  • DOI: https://doi.org/10.1007/JHEP01(2011)037

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