Deformations of Euclidean supersymmetries

Зупник, Б. М.

doi:10.1007/s11232-006-0069-6

Cited by 2 publications

(4 citation statements)

References 21 publications

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“…Indeed such twist were considered for such purpose in [24,25] and [44] and they lead to the noncommutativity of spacetime described by a constant matrix ϑ µν . The novelty of our results here is the use of supersymmetric r-matrices with N = 13 − 16, which leads to Lie-algebraic deformations of the spacetime sector, i.e.…”

Section: Jhep06(2012)154mentioning

confidence: 99%

“…For getting the modified Grassmann variables as in formula (5.13) it is sufficient to consider the simplest canonical supertwist, described by the supersymmetric r-matrices N = 19 − 21 in Table 2. Indeed such twist were considered for such purpose in [22] and [40] and they lead to the noncommutativity of spacetime described by a constant matrix ϑ µν . The novelty of our results here is the use of supersymmetric r-matrices with N = 13 − 16, which leads to Lie-algebraic deformations of the spacetime sector, i.e.…”

Section: Twist-deformed Euclidean Chiral Superspacementioning

confidence: 99%

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$ N = \frac{1}{2} $ deformations of chiral superspaces from new quantum Poincaré and Euclidean superalgebras

Borowiec

Lukierski

Mozrzymas

et al. 2012

J. High Energ. Phys.

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We present a large class of supersymmetric classical r-matrices, describing the supertwist deformations of Poincaré and Euclidean superalgebras. We consider in detail new family of four supertwists of N = 1 Poincaré superalgebra and provide as well their Euclidean counterpart. The proposed supertwists are better adjusted to the description of deformed D = 4 Euclidean supersymmetries with independent left-chiral and right-chiral supercharges. They lead to new quantum superspaces, obtained by the superextension of twist deformations of spacetime providing Lie-algebraic noncommutativity of space-time coordinates. In the Hopf-algebraic Euclidean SUSY framework the considered supertwist deformations provide an alternative to the N = 1 2 SUSY Seiberg's star product deformation scheme.

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Section: Jhep06(2012)154mentioning

confidence: 99%

Section: Twist-deformed Euclidean Chiral Superspacementioning

confidence: 99%

$ N = \frac{1}{2} $ deformations of chiral superspaces from new quantum Poincaré and Euclidean superalgebras

Borowiec

Lukierski

Mozrzymas

et al. 2012

J. High Energ. Phys.

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“…The theory defined on the canonical noncommutative space preserves the Drinfel'd twisted Poincaré symmetry, even though the ordinary Lorentz symmetry is broken. This idea has been extended to supersymmetry and/or conformal symmetry [10,13,12,17,11,16] and there are many applications to field theories, [18] especially a noncommutative theory of gravity [15].…”

Section: Introductionmentioning

confidence: 99%

“…A universal enveloping algebra is an example of a Hopf algebra. The universal enveloping Poincaré algebra is frequently considered in connection with the noncommutative plane [9,10,17]. Generally speaking, Lie algebras are neither unital nor associative.…”

Section: Introductionmentioning

confidence: 99%

Drinfel'd Twisted Superconformal Algebra and the Structure of Unbroken Symmetries

Irisawa¹,

Kobayashi²,

Sasaki³

2007

Progress of Theoretical Physics

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We investigate deformed superconformal symmetries on non(anti)commutative (super)spaces from the point of view of the Drinfel'd twisted symmetries. We classify all possible twist elements derived from an abelian subsector of the superconformal algebra. The symmetry breaking caused by the non(anti)commutativity of the (super)spaces is naturally interpreted as the modification of their coproduct emerging from the corresponding twist element. The remaining unbroken symmetries are determined by the commutative properties of those symmetry generators possessing the twist element. We also comment on non-canonically deformed non(anti)commutative superspaces, particularly those derived from the superconformal twist element F SS . §1. IntroductionThe study of noncommutative spaces has recently attracted considerable interests, because it is thought that they may provide a fundamental basis for a theory of quantum gravity. 4) Superstring theory, which is believed to be the most promising possibility as a consistent theory of quantum gravity, provides a realization of noncommutative space. 3) The simplest noncommutative space, a noncommutative plane, possesses a so-called canonical structure among its coordinates expressed aswhere θ mn is a constant noncommutativity parameter. Note that this canonical noncommutativity breaks the Lorentz invariance of the theory. Field theories on such a noncommutative plane have been intensively studied. (See for example Ref. 4) and references therein.) The space-time noncommutative plane has been generalized to superspaces. 5), 6) The supersymmetric counterpart of Eq. (1) is given by {θ α , θ β } = C αβ = 0,(2) * )

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Deformations of Euclidean supersymmetries

Cited by 2 publications

References 21 publications

$ N = \frac{1}{2} $ deformations of chiral superspaces from new quantum Poincaré and Euclidean superalgebras

$ N = \frac{1}{2} $ deformations of chiral superspaces from new quantum Poincaré and Euclidean superalgebras

Drinfel'd Twisted Superconformal Algebra and the Structure of Unbroken Symmetries

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