$\mathcal {N}=2$
                  N
                  =
                  2
           supersymmetric extension of <i>l</i>-conformal Galilei algebra

Masterov, Ivan

doi:10.1063/1.4732459

Cited by 23 publications

(51 citation statements)

References 76 publications

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“…Concerning the central extensions the results are common for G (2,2) and G (1,2,1) . The superalgebra G (2,2) in d dimensions has a central extension if is a half-integer.…”

Section: Introductionmentioning

confidence: 89%

“…We prove that the centerless, finite N = 2 -superconformal Galilei algebra of ref. [1], expressed in terms of superfields, corresponds to the particular choice of the N = 2 real representation. The novelty here is the introduction of the second superalgebra, associated with the N = 2 chiral representation.…”

Section: Introductionmentioning

confidence: 99%

“…In [2] the (mass and exotic) central extensions of the superalgebra of ref. [1] were given. We prove that mass and exotic central extensions also exist for the chiral supersymmetrization.…”

Section: Introductionmentioning

confidence: 99%

“…For this reason the chiral and real N = 2 supersymmetrizations of the -conformal Galilei algebra are denoted as G (2,2) and G (1,2,1) , respectively. For a non-negative integer or half-integer value of the parameter they admit a consistent truncation as non semi-simple, finite, centerless, Lie superalgebras.…”

Section: Introductionmentioning

confidence: 99%

“…The non-vanishing (anti)commutators of G (2,2) are presented in formulas (2) and (3). The non-vanishing (anti)commutators of G (1,2,1) are given in (2) and (4). Their respective D-module representations (realized by differential operators in d + 1 space-time dimensions) are given in (5) and (6).…”

Section: Introductionmentioning

confidence: 99%

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Chiral and Real N = 2 supersymmetric -conformal Galilei algebras

Aizawa¹,

Kuznetsova²,

Toppan³

2013

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Inequivalent N = 2 supersymmetrizations of the -conformal Galilei algebra in d-spatial dimensions are constructed from the chiral (2, 2) and the real (1, 2, 1) basic supermultiplets of the N = 2 supersymmetry. For non-negative integer and half-integer both superalgebras admit a consistent truncation with a (different) finite number of generators. The real N = 2 case coincides with the superalgebra introduced by Masterov, while the chiral N = 2 case is a new superalgebra.We present D-module representations of both superalgebras. Then we investigate the new superalgebra derived from the chiral supermultiplet. It is shown that it admits two types of central extensions, one is found for any d and half-integer and the other only for d = 2 and integer . For each central extension the centrally extended -superconformal Galilei algebra is realized in terms of its super-Heisenberg subalgebra generators.

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“…Concerning the central extensions the results are common for G (2,2) and G (1,2,1) . The superalgebra G (2,2) in d dimensions has a central extension if is a half-integer.…”

Section: Introductionmentioning

confidence: 89%

Section: Introductionmentioning

confidence: 99%

“…In [2] the (mass and exotic) central extensions of the superalgebra of ref. [1] were given. We prove that mass and exotic central extensions also exist for the chiral supersymmetrization.…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Chiral and Real N = 2 supersymmetric -conformal Galilei algebras

Aizawa¹,

Kuznetsova²,

Toppan³

2013

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$$ \mathcal{N} $$ = 1, 2, 3 ℓ-conformal Galilei superalgebras

Galajinsky

Masterov

2021

J. High Energ. Phys.

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The issue of constructing $$ \mathcal{N} $$ N = 1, 2, 3 supersymmetric extensions of the ℓ-conformal Galilei algebra is reconsidered following the approach in [27]. Drawing a parallel between acceleration generators entering the superalgebra and irreducible supermultiplets of d = 1, $$ \mathcal{N} $$ N -extended superconformal group, a new $$ \mathcal{N} $$ N = 1 ℓ-conformal Galilei superalgebra, two new $$ \mathcal{N} $$ N = 2 variants, and two new $$ \mathcal{N} $$ N = 3 versions are built. Realisations in terms of differential operators in superspace are given.

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N =4 ℓ-conformal Galilei superalgebras inspired by D(2, 1; α) supermultiplets

Galajinsky

Krivonos²

2017

J. High Energ. Phys.

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N = 4 supersymmetric extensions of the -conformal Galilei algebra are constructed by properly extending the Lie superalgebra associated with the most general N = 4 superconformal group in one dimension D(2, 1; α). If the acceleration generators in the superalgebra form analogues of the irreducible (1, 4, 3)-, (2, 4, 2)-, (3, 4, 1)-, and (4, 4, 0)-supermultiplets of D(2, 1; α), the parameter α turns out to be constrained by Jacobi identities. In contrast, if the tower of the acceleration generators resembles a component decomposition of a generic real superfield, which is a reducible representation of D(2, 1; α), α remains arbitrary. An N = 4 -conformal Galilei superalgebra recently proposed in [Phys. Lett. B 771 (2017) 401] is shown to be a particular instance of a more general construction in this work.

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$\mathcal {N}=2$ N = 2 supersymmetric extension of l-conformal Galilei algebra

Abstract: N = 2 supersymmetric extension of the l-conformal Galilei algebra is constructed. A relation between its representations in flat spacetime and in Newton-Hooke spacetime is discussed. An infinite-dimensional generalization of the superalgebra is given.

Cited by 23 publications

References 76 publications

Chiral and Real N = 2 supersymmetric -conformal Galilei algebras

Chiral and Real N = 2 supersymmetric -conformal Galilei algebras

$$ \mathcal{N} $$ = 1, 2, 3 ℓ-conformal Galilei superalgebras

N =4 ℓ-conformal Galilei superalgebras inspired by D(2, 1; α) supermultiplets

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