On Schrödinger superalgebras

Duval, Christian; Horváthy, P. A.

doi:10.1063/1.530521

Cited by 106 publications

(126 citation statements)

References 34 publications

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“…For any pair ε, ε ∈ S c (L), the vector field ξ ε,ε (defined by (25)) is parallel and orthogonal to v. Given another null vector field u with g(u, v) = 1, which always exists locally, it follows that g(X, ξ ε,ε ) = g(X, v)g(ξ ε,ε , u) for any X ∈ X(L), using Consequently, ξ ε,ε = g(ξ ε,ε , u) v, implying that ξ ε,ε and v are collinear. Whence, since they are both parallel, ξ ε,ε = c v for some c ∈ R. Furthermore, the R-symmetry parameter ρ ε,ε (defined above (49)) vanishes identically since ε and ε are parallel.…”

Section: If ε Is Not Parallel Then M Is Locally Isometric To Eithermentioning

confidence: 99%

“…This idea is not new and some previous attempts to define a Lie superalgebra structure for manifolds admitting twistor spinors can be found in [22][23][24] (see also [25] for the construction of Schrödinger superalgebras which do not involve twistor spinors). What distinguishes our construction is the inclusion of non-trivial R-symmetry which turns out to be crucial in order to solve the odd-odd-odd component of the Jacobi identity for the superalgebra.…”

Section: Introductionmentioning

confidence: 99%

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Conformal symmetry superalgebras

Medeiros

Hollands

2013

Class. Quantum Grav.

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ABSTRACT. We show how the rigid conformal supersymmetries associated with a certain class of pseudo-Riemannian spin manifolds define a Lie superalgebra. The even part of this superalgebra contains conformal isometries and constant R-symmetries. The odd part is generated by twistor spinors valued in a particular R-symmetry representation. We prove that any manifold which admits a conformal symmetry superalgebra of this type must generically have dimension less than seven. Moreover, in dimensions three, four, five and six, we provide the generic data from which the conformal symmetry superalgebra is prescribed. For conformally flat metrics in these dimensions, and compact R-symmetry, we identify each of the associated conformal symmetry superalgebras with one of the conformal superalgebras classified by Nahm. We also describe several examples for Lorentzian metrics that are not conformally flat.

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Section: If ε Is Not Parallel Then M Is Locally Isometric To Eithermentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Conformal symmetry superalgebras

Medeiros

Hollands

2013

Class. Quantum Grav.

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“…The purpose of this review article is to give a short summary on the classification of superalgebras with the anisotropic scaling (1) as subalgebras of the following Lie superalgebras (for other Lie superalgebras, see earlier works [14,15]), psu(2,2|4), osp(8|4) and osp (8 * |4), which are concerned with AdS/CFT in type IIB string and M theories. It contains supersymmetric extensions of Schrödinger algebra and Lifshitz algebra.…”

Section: Introductionmentioning

confidence: 99%

Supersymmetric Extensions of Non-Relativistic Scaling Algebras

Sakaguchi

Yoshida

2012

Symmetry

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An exciting subject in string theory is to consider some applications of the AdS/CFT correspondence to realistic systems like condensed matter systems. Since most of such systems are non-relativistic, an anisotropic scaling symmetry with the general value of dynamical critical exponent z plays an important role in constructing the gravity duals for non-relativistic field theories. Supersymmetric extensions of symmetry algebras including the anisotropic scaling are very helpful to consider holographic relations accurately. We give a short summary on the classification of superalgebras with the anisotropic scaling as subalgebras of the following Lie superalgebras, psu(2,2|4), osp(8|4) and osp (8 * |4), which appear in the study of AdS/CFT in type IIB string and M theories. It contains supersymmetric extensions of Schrödinger algebra and Lifshitz algebra.

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“…We relate this model to a classical N = 2 supersymmetric model in (3 + 2) dimensions, giving at the same time an explicit embedding of our 'super-Schrödinger algebra' into osp(2|4) . Note that supersymmetric extensions of the Schrödinger algebra have been discussed several times in the past [2,3,4,15,13,16,17], some of them in the context of supersymmetric quantum mechanics. Here, we consider the problem from a field-theoretical perspective.…”

Section: Introductionmentioning

confidence: 99%

Supersymmetric extensions of Schrödinger-invariance

Henkel¹,

Unterberger²

2006

Nuclear Physics B

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The set of dynamic symmetries of the scalar free Schrödinger equation in d space dimensions gives a realization of the Schrödinger algebra that may be extended into a representation of the conformal algebra in d+2 dimensions, which yields the set of dynamic symmetries of the same equation where the mass is not viewed as a constant, but as an additional coordinate. An analogous construction also holds for the spin-1 2 Lévy-Leblond equation. An N = 2 supersymmetric extension of these equations leads, respectively, to a 'super-Schrödinger' model and to the (3|2)-supersymmetric model. Their dynamic supersymmetries form the Lie superalgebras osp(2|2)⋉ sh(2|2) and osp(2|4), respectively. The Schrödinger algebra and its supersymmetric counterparts are found to be the largest finite-dimensional Lie subalgebras of a family of infinite-dimensional Lie superalgebras that are systematically constructed in a Poisson algebra setting, including the Schrödinger-NeveuSchwarz algebra sns (N ) with N supercharges.Covariant two-point functions of quasiprimary superfields are calculated for several subalgebras of osp(2|4). If one includes both N = 2 supercharges and time-inversions, then the sum of the scaling dimensions is restricted to a finite set of possible values.

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On Schrödinger superalgebras

Abstract: Abstract.We construct, using the supersymplectic framework of Berezin, Kostant and others, two types of supersymmetric extensions of the Schrödinger algebra (itself a conformal extension of the Galilei algebra). An 'I-type' extension exists in any space dimension, and for any

Cited by 106 publications

References 34 publications

Conformal symmetry superalgebras

Conformal symmetry superalgebras

Supersymmetric Extensions of Non-Relativistic Scaling Algebras

Supersymmetric extensions of Schrödinger-invariance

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