Unextended superfields in extended supersymmetry

In extended supersymmetry, we discuss the advantages of unextended superfields over extended ones and component fields. We show how to derive from the extended formalism the unextended superfields, and their extended supersymmetry transformations in unextended-superfield form.     

Non-linear representations of extended supersymmetry with central charges

A new class of non-linear representations ofN extended supersymmetry is found. These non-linear realizations extend the Volkov-Akulov non-linear realizations to include central charges which can also be non-linearly realized. The general construction of the corresponding non-linear Lagrangians is presented. The coupling toN extended supergravity provides the simultaneous occurrence of the Higgs and super-Higgs effects. The corresponding formulae for spin-3/2 gravitinos and spin-1 vector boson masses are derived.     

All linear unitary irreducible representations of De Sitter supersymmetry with positive energy

All linear unitary irreducible representations of the graded Lie algebra osp (4.1) with positive energy are calculated by acting with the odd elements on a vacuum state. With the exception of the Dirac supermultiplet, the result corresponds to the representations of Poincaré supersymmetry.     

N=4 conformal supergravity and irreducible superfields

Among irreducible N=4 superfields, into which can be decomposed a general N=4 scalar superfield, we select a superfield with 128 + 128 components which characterizes a conformai N=4 supercurrent. The obtained superfield is used in order to explicitly construct the linearized N = 4 conformai supergravity outside the mass shell in N = 4 superspace.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 83–87, September, 1989.     

Representations of N = 4 supersymmetry on superfields

We determine all of the irreducible representations (irreps) of the extended supersymmetry algebra (for N = 2 and 4) on superfields with arbitrary external spin in terms of the associated eigenvalues of suitable Casimirs of enlarged algebras. Detailed results are presented for the scalar, spinor and vector superfield cases. The component content of the corresponding irreps are also discussed by means of suitable basis functions.     

A six-dimensional superspace approach to extended superfields

We present an improved formalism for treating six-dimensional superspace and apply it to writing linearized N = 2 Yang-Mills theory and the N = 2 relaxed hypermultiplet in SU(2) covariant forms that are simpler than the known four-dimensional forms.     

Supercurrents in extended supersymmetry

Using the generalization of Noether's theorem to superspace, spinor superfields in extended superspace are derived that satisfy generalized conservation equations. These spinor superfields are superspace moments involving the superconformal parameters of vector indexed supercurrents as in the unextended case. The vector indexed supercurrents obtained in this fashion are simply related to the usual scalar supercurrents in extended superspace.     

Analytical constraints in extended supersymmetry

Starting from the deep relation between the system of numbers and extended supersymmetry we can obtain analytical constraints for superfields.Presented at the International Symposium Selected Topics in Quantum Field Theory and Mathematical Physics, Bechyn, Czechoslovakia, June 14–19, 1981.     

Superconformal invariants and extended supersymmetry

The superconformal invariants in analytic superspace are found. Superconformal invariance is shown to imply that the Green's functions of analytic operators are invariant holomorphic sections of a line bundle on a product of certain harmonic superspaces. It is argued that the correlation functions for a class of sufficiently low dimension gauge invariant operators in N = 2 and N = 4 supersymmetric Yang-Mills theory can be evaluated up to constants.     

Basis of irreducible representations of orthogonal groups

A method for constructing a basis of irreducible representations of unitary groupsU _n is generalized to orthogonal groupsO _n. The corresponding algorithm is given for the chain for groupsU _n O _n and also for the chain which is of great relevance in physics.The constructed basis is used for the calculation of the fractional six-particle parentage coefficients for separation of one-, two- and three-particle wave functions. All possible states with excitation quantaN2 are taken into account. The present results, together with previous work, are used for the investigation of the six-quark system, in particular for calculating theD-state probability in the ground state of this system.     

Two-parameter extended Hubbard Hamiltonian with supersymmetry

We investigate under which circumstances extended Hubbard models, including bond-charge, exchange, and pair-hopping terms, are invariant under gl (2,1) superalgebra. This happens for a two-parameter Hamiltonian which includes as particular cases the t - J, the EKS and the one-parameter BGLZ Hamiltonians, all integrable in one dimension. We show that the two parameter Hamiltonian can be recasted as the sum of the BGLZ Hamiltonian plus the graded permutation operator of electronic states on neighbouring sites. The integrability of the corresponding one-dimensional model is discussed. Received: 17 February 1998 / Received in final form: 6 March 1998 / Accepted: 17 April 1998     

General massive multiplets in extended supersymmetry

We consider the extended Poincaré superalgebra in four dimensions with general central charge operators. We find the invariance of this algebra and the particle supermultiplets with their internal symmetry properties. Central charges obtained by dimensional reduction appear as a special case in this classification.     

Unitary irreducible representations ofSU(2,2)

Using a Lie algebra method based on works byHarish-Chandra, several series of unitary, irreducible representations of the groupSU(2,2) are obtained.     

On the irreducible representations of the lorentz group

All continuous irreducible representations of the SL(2, C) group (as given by Naimark) are obtained by means of methods developed by Harish-Chandra and Kihlberg. The analysis is done in the SU(2) basis and a single closed expression for the matrix elements of the noncompact generators for an arbitrary irreducible representation of SL(2, C) is given. For the unitary irreducible representations the scalar product for each irreducible Hilbert space is found explicitly. The connection between the unitary irreducible representations of SL(2, C) and those of

is discussed by means of Inönü and Wigner contraction procedure and the Gell-Mann formula. Finally, due to physical interest, the addition of a four-vector operator to SL(2, C) unitary irreducible representations in a minimal way is considered; and all group extensions of the parity and time reversal operators by SL(2, C) are explicitly obtained and some aspects of their representations are treated.     

On irreducible representations of the ultrahyperbolic BMS group

The ordinary Bondi–Metzner–Sachs (BMS) group B is the common asymptotic symmetry group of all asymptotically flat Lorentzian space–times. As such, B is the best candidate for the universal symmetry group of General Relativity. However, in studying quantum gravity, space–times with signatures other than the usual Lorentzian one, and complex space–times, are frequently considered. Generalisations of B appropriate to these other signatures have been defined earlier. Here, the generalisation B(2,2) appropriate to the ultrahyperbolic signature (+,+,−,−) is described in detail, and the irreducible unitary representations (IRs) of B(2,2) are analysed. It is proved that all induced IRs of B(2,2) arise from IRs of compact “little groups”. These little groups, which are closed subgroups of K=SO(2)×SO(2), are classified here in detail, with particular attention paid to those of infinite order.     

On a method of constructing irreducible multiplier representations

A systematic method is presented for constructing the irreducible multiplier representations (ray representations) of a class of finite groups corresponding to a given factor system. The method consists in first identifying a normal subgroup of prime index, classifying its irreducible multiplier representations into orbits and then inducing the required representations from these orbits. The proposed technique finds useful application in solid state physics where irreducible multiplier representations of the point group underlying the group of the wave vector are frequently required.     

Observables in topological Yang-Mills theorieswith extended shift supersymmetry

We present a complete classification, at the classical level, of the observables of topological Yang-Mills theories with an extended shift supersymmetry of N generators, in any space-time dimension. The observables are defined as the Yang-Mills BRST cohomology classes of shift supersymmetry invariants. These cohomology classes turn out to be solutions of an N-extension of Witten's equivariant cohomology. This work generalizes results known in the case of shift supersymmetry with a single generator. Received: 8 March 2005, Published online: 21 October 2005 Supported in part by the Conselho Nacional de Desenvolvimento Científico e Tecnológico CNPq, Brazil