### Abstract

In three dimensions, every known N=4 supermultiplet has an off-shell completion. However, there is no off-shell N=4 formulation for the known extended superconformal Chern-Simons (CS) theories with eight and more supercharges. To achieve a better understanding of this issue, we provide N=4 superfield realizations for the equations of motion which correspond to various N=4 and N=6 superconformal CS theories, including the Gaiotto-Witten theory and the Aharony-Bergman-Jafferis-Maldacena (ABJM) theory. These superfield realizations demonstrate that the superconformal CS theories with N≥4 (except for the Gaiotto-Witten theory) require a reducible long N=4 vector multiplet, from which the standard left and right N=4 vector multiplets are obtained by constraining the field strength to be either self-dual or antiself-dual. Such a long multiplet naturally originates upon reduction of any off-shell N>4 vector multiplet to N=4 superspace. For the long N=4 vector multiplet we develop a prepotential formulation. It makes use of two prepotentials being subject to the constraint which defines the so-called hybrid projective multiplets introduced in the framework of N=4 supergravity-matter systems in arXiv:1101.4013. We also couple N=4 superconformal CS theories to N=4 conformal supergravity.

Original language | English |
---|---|

Article number | 105007 |

Journal | Physical Review D - Particles, Fields, Gravitation and Cosmology |

Volume | 92 |

Issue number | 10 |

DOIs | |

Publication status | Published - 4 Nov 2015 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Nuclear and High Energy Physics
- Physics and Astronomy (miscellaneous)

### Cite this

*Physical Review D - Particles, Fields, Gravitation and Cosmology*,

*92*(10), [105007]. https://doi.org/10.1103/PhysRevD.92.105007

**Superconformal Chern-Simons-matter theories in N=4 superspace.** / Kuzenko, Sergei M.; Samsonov, Igor B.

Research output: Contribution to journal › Article

*Physical Review D - Particles, Fields, Gravitation and Cosmology*, vol. 92, no. 10, 105007. https://doi.org/10.1103/PhysRevD.92.105007

}

TY - JOUR

T1 - Superconformal Chern-Simons-matter theories in N=4 superspace

AU - Kuzenko, Sergei M.

AU - Samsonov, Igor B.

PY - 2015/11/4

Y1 - 2015/11/4

N2 - In three dimensions, every known N=4 supermultiplet has an off-shell completion. However, there is no off-shell N=4 formulation for the known extended superconformal Chern-Simons (CS) theories with eight and more supercharges. To achieve a better understanding of this issue, we provide N=4 superfield realizations for the equations of motion which correspond to various N=4 and N=6 superconformal CS theories, including the Gaiotto-Witten theory and the Aharony-Bergman-Jafferis-Maldacena (ABJM) theory. These superfield realizations demonstrate that the superconformal CS theories with N≥4 (except for the Gaiotto-Witten theory) require a reducible long N=4 vector multiplet, from which the standard left and right N=4 vector multiplets are obtained by constraining the field strength to be either self-dual or antiself-dual. Such a long multiplet naturally originates upon reduction of any off-shell N>4 vector multiplet to N=4 superspace. For the long N=4 vector multiplet we develop a prepotential formulation. It makes use of two prepotentials being subject to the constraint which defines the so-called hybrid projective multiplets introduced in the framework of N=4 supergravity-matter systems in arXiv:1101.4013. We also couple N=4 superconformal CS theories to N=4 conformal supergravity.

AB - In three dimensions, every known N=4 supermultiplet has an off-shell completion. However, there is no off-shell N=4 formulation for the known extended superconformal Chern-Simons (CS) theories with eight and more supercharges. To achieve a better understanding of this issue, we provide N=4 superfield realizations for the equations of motion which correspond to various N=4 and N=6 superconformal CS theories, including the Gaiotto-Witten theory and the Aharony-Bergman-Jafferis-Maldacena (ABJM) theory. These superfield realizations demonstrate that the superconformal CS theories with N≥4 (except for the Gaiotto-Witten theory) require a reducible long N=4 vector multiplet, from which the standard left and right N=4 vector multiplets are obtained by constraining the field strength to be either self-dual or antiself-dual. Such a long multiplet naturally originates upon reduction of any off-shell N>4 vector multiplet to N=4 superspace. For the long N=4 vector multiplet we develop a prepotential formulation. It makes use of two prepotentials being subject to the constraint which defines the so-called hybrid projective multiplets introduced in the framework of N=4 supergravity-matter systems in arXiv:1101.4013. We also couple N=4 superconformal CS theories to N=4 conformal supergravity.

UR - http://www.scopus.com/inward/record.url?scp=84948808913&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84948808913&partnerID=8YFLogxK

U2 - 10.1103/PhysRevD.92.105007

DO - 10.1103/PhysRevD.92.105007

M3 - Article

AN - SCOPUS:84948808913

VL - 92

JO - Physical review D: Particles and fields

JF - Physical review D: Particles and fields

SN - 1550-7998

IS - 10

M1 - 105007

ER -