super-Poincare Algebra Research Articles

Wess-Zumino Term for the AdS Superstring and Generalized Inonu-Wigner Contraction

We examine a Wess-Zumino term, written in bilinear of superinvariant currents, for a superstring in anti-de Sitter (AdS) space. The standard Inonu-Wigner contraction does not give the correct flat limit but gives zero. This originates from the fact that the fermionic metric of the super-Poincare group is degenerate. We propose a generalization of the Inonu-Wigner contraction which reduces the super-AdS group to the "nondegenerate" super-Poincare group, therefore it gives a correct flat limit of this Wess-Zumino term. We also discuss the M-algebra obtained by this generalized Inonu-Wigner contraction from osp(1|32).

The simplest superalgebras in two, three, four and five dimensions

Abstract The simplest super-Poincare algebras in two through five space–time dimensions with varying signatures are determined. The possibility of employing more than one definition of charge conjugation is considered. The Hilbert space associated with the Fermionic creation and annihilation operators is examined in each case to see what conditions must be met for it to be positive definite. Representations of the algebras are provided in a number of the spaces considered.

Superon-quintet and graviton model for supersymmetric spacetime and matter

By using the irreducible representation of N = 10 extended Super-Poincare algebra, an attempt to interpret the quarks, the leptons and the gauge bosons except the graviton as the composites of more fundamental objects with spin 1/2, superon quintet, is presented. All the local gauge interactions of GUTs are investigated systematically by using the superon diagrams. The stability of the proton and the suppression of the flavour changing neutral currents are understood naturally in the superon pictures of GUTs. The fundamental action of the model is proposed and the uniqueness of the model is pointed out.

Graded Poincare Algebra, Spin-Vector Gauge Fields and Gauge Theory of Gravity

A gauge theory of gravity based on the complexified internal 4-dimensional graded Poincare group GPc 4 [ is investigated. The algebra of GP~[ is constructed from the dif­ ferential operators in spin vector space and resembles the super Poincare algebra. Without Grassmann coordinates, anticommuting spin vector gauge fields i.pa A (A = 1,2) are introduced, as well as the soldering forms aa AB'. Using the spin vector gauge fields, another Lagrangian density, which is the spinor partner of Jacobson and Smolin, is proposed.

Massive superparticle in d=2+1 and sigma model solitons

The authors show that the gauge-fixed N=2, d=2+1 massive superparticle has an N=4 worldline supersymmetry that is partially broken down to N=2 by the central charge in the supersymmetry algebra. The fact that this model has partial breaking of supersymmetry implies that it is the leading term in the effective action for the solitons of N=2 supersymmetric, 2+1-dimensional sigma models that saturate a Bogomol'nyi bound. Invariant actions can be obtained using the method of non-linear realisations applied to the N=2 super-Poincare group in three dimensions. By explicitly including the central charge in the algebra, the superparticle action appears as a Wess-Zumino-type term. They also construct a supersymmetry extension of a term quadratic in the extrinsic curvature of the worldline, which corresponds to the first correction in the effective action of the soliton.

VECTOR-SPINOR SUPERALGEBRA AND GOLDSTONE SPIN −3/2 FERMIONS

The super-Poincare algebra of the generators belonging to the irreducible (1, 1/2) + (1/2, 1) representation of the Lorentz group is constructed. It is shown that the nonlinear realizations of the vector spinor superalgebra lead to a goldstone fermion carrying spin −3/2. A phenomenological Lagrangian is constructed that describes interactions of the spin −3/2 goldstone fermion with itself.

The quantisation of the massiveN=2 superparticle

An Azcarraga-Lukierski supersymmetric particle model, which is invariant with respect to theN=2 extended SuperPoincare group, is quantised by the method of Dirac brackets. The central charges, which satisfy the spin reducing conditions, are conjugate to additional bosonic coordinates in the superspace. The resulting superwavefunction doublet is in one-to-one correspondence with the superfield expansion of Sohnius describing the Fayet hypermultiplet.

SUPERALGEBRAS WITH FERMIONIC GENERATORS OTHER THAN SPIN-1/2

The possibility of constructing graded Lie algebras of higher spin fermionic generators is entertained. The super Poincare algebra of the generators belonging to the (1, 1/2)+(1/2, 1) representation of the Lorentz group is constructed. The closure of the algebra is demonstrated.

The superconformal algebra in higher dimensions

The superconformal algebra for 4/4N-dimensional super-Minkowski space (d=4) can be identified with the simple superalgebra su (2,2/N). For even-dimension d=5,6 the superconformal algebra can be identified with a real form of the simple superalgebras F(4), D(4,1) respectively in Kac's classification. For even-dimension d>-7 it is impossible to define a superconformal algebra satisfying three natural conditions: (1) it acts as infinitesimal automorphisms on super-Minkowski space; (2) this action extends the natural action of the super-Poincare algebra; (3) when the action of the even part of the superconformal algebra is reduced to an infinitesimal action on ordinary Minkowski space, it extends the natural action of the conformal algebra so (2, d).

Cohomology and deformations of lie superalgebras

Following Leites, we define a cohomology for Lie superalgebras. A number of combinatorial identities are presented as well as two theorems which prove to be very useful in calculations. We then introduce the notion of deformations of Lie superalgebras and look at the deformations of the super-Poincare algebra and of osp(4/2).

The super-Poincar� algebra and the scalar superfield in ten dimensions

The super-Poincare algebra in 10 dimensions is examined. The differences with respect to the other cases are pointed out. In particular, the scalar superfield is considered in detail as an example.

Supersymmetric particles inN=2superspace: Phase-space variables and Hamiltonian dynamics

We consider a reparametrization-invariant model recently proposed based on the N-extended super-Poincare group with central charges, which leads to trajectories on the N-extended Salam-Strathdee superspace. The case N = 2 is discussed in detail. We show that the N = 2 model is invariant under four real supergauge transformations generated by first-class odd constraints which imply the Dirac equation. We introduce one bosonic (which fixes the reparametrization) and four real spinorial (which fix the supergauges) gauge conditions and calculate the Dirac brackets for the remaining unconstrained variables (x,p,theta/sup ..cap alpha../,theta-bar/sup alpha-dot/). The equations of motion are written in Hamiltonian form, with HproportionalTr)Q/sub alphai/,Q-bar/sub beta-doti/) and correspond to the Heisenberg equations of the (first) quantized theory.

Fibre bundles and supergravity

We present a simple derivation of on-shellN=2 supergravity by using fibre bundle analysis; this is done by introducing a central charge as a part of the connection in a principal bundle whose structure group is the super-Poincare group. As a consequence there is a non-trivial generalization of the supersymmetry transformations.

Geometric origin of central charges

The complete set of N(N-1) central charge generators for the D=4 N-extended super-Poincare algebra is obtained by suitable contraction of the OSp(2N;4) superalgebra. The superspace realisations of the spinorial generators with central charges are derived. The conjugate set of N(N-1) additional bosonic superspace coordinates is introduced in a unique and geometric way.

Geometry of superspace and local supersymmetry

We briefly review the theory of general relativity in superspace and show how the theory may be interpreted from the view of a superfiber bundle. It is shown that this superfiber, however, does not possess, as its structural group, the fourteen-parameter group of global supersymmetry, the super Poincare group. Starting from an ansatz which is suggested by superspace general relativity, a second superfiber bundle theory is constructed which does possess the super Poincare group as its structural group.