### Abstract

We construct the classical action of the Aharony-Bergman-Jafferis-Maldacena (ABJM) model in the = 3, d = 3 harmonic superspace. In such a formulation three out of six supersymmetries are realized off shell while the other three mix the superfields and close on shell. The superfield action involves two hypermultiplet superfields in the bifundamental representation of the gauge group and two Chern-Simons gauge superfields corresponding to the left and right gauge groups. The = 3 superconformal invariance allows only for a minimal gauge interaction of the hypermultiplets. Amazingly, the correct sextic scalar potential of ABJM emerges after the elimination of auxiliary fields. Besides the original U(N) × U(N) ABJM model, we also construct = 3 superfield formulations of some generalizations. For the SU(2) × SU(2) case we give a simple superfield proof of its enhanced = 8 supersymmetry and SO(8) R-symmetry.

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

Article number | 096 |

Journal | Journal of High Energy Physics |

Volume | 2009 |

Issue number | 3 |

DOIs | |

Publication status | Published - 2009 |

### Fingerprint

### Keywords

- Chern-Simons theories
- Extended supersymmetry
- Superspaces
- Supersymmetric gauge theory

### ASJC Scopus subject areas

- Nuclear and High Energy Physics

### Cite this

*Journal of High Energy Physics*,

*2009*(3), [096]. https://doi.org/10.1088/1126-6708/2009/03/096

**ABJM models in N= 3 harmonic superspace.** / Buchbinder, I. L.; Ivanov, E. A.; Lechtenfeld, O.; Pletnev, N. G.; Samsonov, I. B.; Zupnik, B. M.

Research output: Contribution to journal › Article

*Journal of High Energy Physics*, vol. 2009, no. 3, 096. https://doi.org/10.1088/1126-6708/2009/03/096

}

TY - JOUR

T1 - ABJM models in N= 3 harmonic superspace

AU - Buchbinder, I. L.

AU - Ivanov, E. A.

AU - Lechtenfeld, O.

AU - Pletnev, N. G.

AU - Samsonov, I. B.

AU - Zupnik, B. M.

PY - 2009

Y1 - 2009

N2 - We construct the classical action of the Aharony-Bergman-Jafferis-Maldacena (ABJM) model in the = 3, d = 3 harmonic superspace. In such a formulation three out of six supersymmetries are realized off shell while the other three mix the superfields and close on shell. The superfield action involves two hypermultiplet superfields in the bifundamental representation of the gauge group and two Chern-Simons gauge superfields corresponding to the left and right gauge groups. The = 3 superconformal invariance allows only for a minimal gauge interaction of the hypermultiplets. Amazingly, the correct sextic scalar potential of ABJM emerges after the elimination of auxiliary fields. Besides the original U(N) × U(N) ABJM model, we also construct = 3 superfield formulations of some generalizations. For the SU(2) × SU(2) case we give a simple superfield proof of its enhanced = 8 supersymmetry and SO(8) R-symmetry.

AB - We construct the classical action of the Aharony-Bergman-Jafferis-Maldacena (ABJM) model in the = 3, d = 3 harmonic superspace. In such a formulation three out of six supersymmetries are realized off shell while the other three mix the superfields and close on shell. The superfield action involves two hypermultiplet superfields in the bifundamental representation of the gauge group and two Chern-Simons gauge superfields corresponding to the left and right gauge groups. The = 3 superconformal invariance allows only for a minimal gauge interaction of the hypermultiplets. Amazingly, the correct sextic scalar potential of ABJM emerges after the elimination of auxiliary fields. Besides the original U(N) × U(N) ABJM model, we also construct = 3 superfield formulations of some generalizations. For the SU(2) × SU(2) case we give a simple superfield proof of its enhanced = 8 supersymmetry and SO(8) R-symmetry.

KW - Chern-Simons theories

KW - Extended supersymmetry

KW - Superspaces

KW - Supersymmetric gauge theory

UR - http://www.scopus.com/inward/record.url?scp=67649437310&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=67649437310&partnerID=8YFLogxK

U2 - 10.1088/1126-6708/2009/03/096

DO - 10.1088/1126-6708/2009/03/096

M3 - Article

AN - SCOPUS:67649437310

VL - 2009

JO - Journal of High Energy Physics

JF - Journal of High Energy Physics

SN - 1126-6708

IS - 3

M1 - 096

ER -