Quaternionic structures, supertwistors and fundamental superspaces (original) (raw)

Physics Letters B, 1988

N) bosonic and 4Nfermionic coordinates are obtained from supersymmetric extension of twistor formalism. The description of real superspaces, with real Minkowski coordinates, is also considered. The case N=2, k= I, corresponding to N=2 harmonic superspace of Ogievetski and Sokchaczev, is discussed in some detail.

supersymmetric quaternionic mechanics

Physics Letters B, 2005

We construct N = 8 supersymmetric mechanics with four bosonic end eight fermionic physical degrees of freedom. Starting from the most general N = 4 superspace action in harmonic superspace for the (4,8,4) supermultiplet we find conditions which make it N = 8 invariant. We introduce in the action Fayet-Iliopoulos terms which give rise to potential terms. We present the action in components and give explicit expressions for the Hamiltonian and Poisson brackets. Finally we discuss the possibility of N = 9 supersymmetric mechanics.

SUPERSYMMETRIC LORENTZ INVARIANT DEFORMATIONS OF SUPERSPACES

Modern Physics Letters A, 2006

Lorentz invariant supersymmetric deformations of superspaces based on Moyal star product parametrized by Majorana spinor λ a and Ramond grassmannian vector ψ m = − 1 2 (θγ m λ) in the spinor realization [35] are proposed. The map of supergravity background into composite supercoordinates: (B −1 mn , Ψ a m , C ab ) ↔ (iψ m ψ n , ψ m λ a , λ a λ b ) valid up to the second order corrections in deformation parameter h and transforming the background dependent Lorentz noninvariant (anti)commutators of supercoordinates into their invariant Moyal brackets is revealed. We found one of the deformations to depend on the axial vector ψ 1m = 1 2 (θγ m γ 5 λ) and to vanish for the θ components with the same chiralities. The deformations in the (super)twistor picture are discussed.

A Linear Realization for the New Space–Time Superalgebras in 10 and 11 Dimensions

Modern Physics Letters A, 1997

The new extensions of the Poincaré superalgebra recently found in ten and eleven dimensions are shown to admit a linear realization. The generators of the nonlinear and linear group transformations are shown to fall into equivalent representations of the superalgebra. The parametrization of the coset space G/H, with G a given extended supergroup and H the Lorentz subgroup, that corresponds to the linear transformations is presented.

Quaternionic quantum mechanics for N = 1, 2, 4 supersymmetry

Beni-Suef University Journal of Basic and Applied Sciences

Background Quaternions have emerged as powerful tools in higher-dimensional quantum mechanics as they provide homogeneous four-dimensional structure in quantum field theories, offer compact representations, and incorporate spin naturally. Quantum field theories then lead to the unification of fundamental interactions so the use of quaternion becomes necessary when we are dealing with higher-dimensional theories. On the other hand, supersymmetry is the theory of bosons and fermions and is an essential constituent of grand unified theories. The use of quaternion in supersymmetric field theories provides an excellent framework for higher-dimensional unification theories. Result A complete theory for supersymmetric quaternionic quantum mechanics has been constructed for N = 1, 2, 4 supersymmetry in terms of one, two, and four supercharges and Hamiltonians, respectively. It has been shown that N = 4 SUSY is the quaternionic extension of the N = 2 complex SUSY and N = 1 real SUSY; also sp...

N=8 supersymmetric quaternionic mechanics

Physics Letters B, 2005

Reparametrization of supergroup: Superspace as a vectorspace

Acta Physica Hungarica, 1983

In this paper we show that, with reparametrization of supergroup, superspace as the homogeneous space ofit will be linearized, superfield will be defined uniquely, vector coordinates and spinor coordinates will play the equal r61e... We can list all possible subgroups of supergroup easily in this way of parametrization. The reprr of this algebra will be given. The linearization of superspace would lead to new approaches to construct geometrical structures on it. The Abelian translation group would make easier the construction of the harmonic analysis on it. Last of all, the SU(N) internal symmetry of extended superunified theories would be manifest in these models.

Quaternionic structures, supertwistors and fundamental superspaces (original) (raw)

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