$ \mathcal{N} = 8 $ superspace constraints for three-dimensional gauge theories

Samtleben, Henning; Wimmer, Robert

doi:10.1007/jhep02(2010)070

Cited by 22 publications

(41 citation statements)

References 74 publications

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“…We will only formulate the equations of motion for N ≥ 4 superconformal CS theories in N = 4 superspace. Similar on-shell realisations in N = 6 and N = 8 superspaces have been given in [19,20,21]. This note is organised as follows.…”

Section: Introductionmentioning

confidence: 81%

Superconformal Chern-Simons-matter theories inN=4superspace

Kuzenko

Samsonov

2015

Phys. Rev. D

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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 realisations for the equations of motion which correspond to various N = 4 and N = 6 superconformal CS theories, including the Gaiotto-Witten theory and the ABJM theory. These superfield realisations 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 anti self-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.

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Section: Introductionmentioning

confidence: 81%

Superconformal Chern-Simons-matter theories inN=4superspace

Kuzenko

Samsonov

2015

Phys. Rev. D

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“…We follow [91] Introducing the real symmetric matrices (σ µ ) αβ := (γ µ ) ρ β ǫ ρα and (σ µ ) αβ := (ǫ · σ µ · ǫ) αβ = −ǫ βρ (γ µ ) α ρ , a three vector in spinor notation writes as a symmetric real matrix as…”

Section: Appendicesmentioning

confidence: 99%

Deformed twistors and higher spin conformal (super-)algebras in four dimensions

Govil

Günaydın

2015

J. High Energ. Phys.

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Massless conformal scalar field in d = 4 corresponds to the minimal unitary representation (minrep) of the conformal group SU(2, 2) which admits a one-parameter family of deformations that describe massless fields of arbitrary helicity. The minrep and its deformations were obtained by quantization of the nonlinear realization of SU(2, 2) as a quasiconformal group in arXiv:0908.3624. We show that the generators of SU(2, 2) for these unitary irreducible representations can be written as bilinears of deformed twistorial oscillators which transform nonlinearly under the Lorentz group and apply them to define and study higher spin algebras and superalgebras in AdS 5 . The higher spin (HS) algebra of Fradkin-Vasiliev type in AdS 5 is simply the enveloping algebra of SU(2, 2) quotiented by a two-sided ideal (Joseph ideal) which annihilates the minrep. We show that the Joseph ideal vanishes identically for the quasiconformal realization of the minrep and its enveloping algebra leads directly to the HS algebra in AdS 5 . Furthermore, the enveloping algebras of the deformations of the minrep define a one parameter family of HS algebras in AdS 5 for which certain 4d covariant deformations of the Joseph ideal vanish identically. These results extend to superconformal algebras SU(2, 2|N ) and we find a one parameter family of HS superalgebras as enveloping algebras of the minimal unitary supermultiplet and its deformations. Our results suggest the existence of a family of (supersymmetric) HS theories in AdS 5 which are dual to free (super)conformal field theories (CFTs) or to interacting but integrable (supersymmetric) CFTs in 4d. We also discuss the corresponding picture in HS algebras in AdS 4 where the corresponding 3d conformal group Sp(4, R) admits only two massless representations (minreps), namely the scalar and spinor singletons.

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“…See[23] for similar expansions in the case of three-dimensional supersymmetric Chern-Simons theories in the context of M2-branes.…”

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confidence: 98%

Non-Abelian Tensor Multiplet Equations from Twistor Space

Sämann

Wolf

2014

Commun. Math. Phys.

139

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We establish a Penrose-Ward transform yielding a bijection between holomorphic principal 2-bundles over a twistor space and non-Abelian self-dual tensor fields on six-dimensional flat space-time. Extending the twistor space to supertwistor space, we derive sets of manifestly N = (1,0) and N = (2,0) supersymmetric non-Abelian constraint equations containing the tensor multiplet. We also demonstrate how this construction leads to constraint equations for non-Abelian supersymmetric self-dual strings. © 2014 Springer-Verlag Berlin Heidelberg

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$ \mathcal{N} = 8 $ superspace constraints for three-dimensional gauge theories

Cited by 22 publications

References 74 publications

Superconformal Chern-Simons-matter theories inN=4superspace

Superconformal Chern-Simons-matter theories inN=4superspace

Deformed twistors and higher spin conformal (super-)algebras in four dimensions

Non-Abelian Tensor Multiplet Equations from Twistor Space

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