ABJM models in N= 3 harmonic superspace

I. L. Buchbinder, E. A. Ivanov, O. Lechtenfeld, N. G. Pletnev, I. B. Samsonov, B. M. Zupnik

Research output: Contribution to journal › Article

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	https://doi.org/10.1088/1126-6708/2009/03/096
Publication status	Published - 2009

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Keywords

Chern-Simons theories
Extended supersymmetry
Superspaces
Supersymmetric gauge theory

ASJC Scopus subject areas

Nuclear and High Energy Physics

Cite this

Buchbinder, I. L., Ivanov, E. A., Lechtenfeld, O., Pletnev, N. G., Samsonov, I. B., & Zupnik, B. M. (2009). ABJM models in N= 3 harmonic superspace. Journal of High Energy Physics, 2009(3), [096]. https://doi.org/10.1088/1126-6708/2009/03/096

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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.",

keywords = "Chern-Simons theories, Extended supersymmetry, Superspaces, Supersymmetric gauge theory",

author = "Buchbinder, {I. L.} and Ivanov, {E. A.} and O. Lechtenfeld and Pletnev, {N. G.} and Samsonov, {I. B.} and Zupnik, {B. M.}",

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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

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KW - Supersymmetric gauge theory

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10.1088/1126-6708/2009/03/096