Zbigniew Hasiewicz

Seven-dimensional De Sitter and six-dimensional conformal supersymmetries

Abstract The N-extended D=7 De Sitter algebras UαU(4, N;H) with bosonic sector SO(6,2) × Sp(N), describing also N-extended D=6 superconformal symmetries are given. The quaternionic structure of real representation is described by three real quaternionic Majorana conditions. We conjecture that N=2 D=7 De Sitter supergroup UαU(4,2;H) describes the supersymmetries of the vacuum solution for D=11 supergravity, with the space-time described by seven-dimensional De Sitter space and internal space S4.

Superconformal algebras with quadratic nonlinearity

Abstract We present new superconformal algebras, containing both bosonic and fermionic supersymmetries, based on the superalgebras OSp(m|2n) and U(m|n). They contain as special cases the previously known series based on O( m ), U( m ) and Sp(2 n ) Lie algebras. The case U(n+2|n) is special, in that it can be reduced to SU(n+2|n), generalising the standard N = 4 superconformal algebra.

Non-critical light-cone string

A free string quantum model is constructed directly in the light-cone variables in the range of dimensions 1 < D < 25. The longitudinal degrees of freedom are described by an abstract Verma module with the central charge restricted by the requirement of closure of the non-linear realization of the Poincare algebra. The spin content of the model is analyzed. In particular for D = 4 the explicit formulae for the character generating functions of the open and closed strings are given and the spin spectrum of the first twelve excited levels is calculated. It is shown that for the space-time dimension in the range 1 < D < 25 this light-cone quantum model is equivalent to the critical massive string and to the non-critical Nambu-Goto string.

Classical and quantum massive string

Abstract The classical and the quantum massive string model based on a modified BDHP action is analyzed in the range of dimensions 1

Supersymmetrized D = 11 de-sitter-like algebra from octonions

Abstract We consider S 7 as a soft Lie group manifold. We introduce a graded de-Sitter-like algebra in D = 11 as described by the octonionic extension of OSp (1;4), with bosomic sector parametrized as (SO(10, 2)/G 2 × S 7 . We provide constructive remarks concerning the meaning of the octonionic extensions of Lie algebras and Lie superalgebras.

Spectrum generating algebra and no ghost theorem for fermionic massive string

Abstract The covariant operator quantization of the ordinary free spinning BDH string modified by adding the supersymmetric Liouville sector is analysed in the even target space dimensions d = 2, 4, 6, 8. The spectrum generating algebra for this model is constructed and a general version of the no-ghost theorem is proven. The counterpart of the GSO projection leads to a family of tachyon-free unitary free string theories. One of these models is equivalent to the non-critical Ramond-Neveu-Schwarz spinning string truncated in the Neveu-Schwarz sector to the tachyon-free eigenspace of the fermion parity operator.

Anomalous brst complexes for noncritical massive strings

It is shown that the BRST resolution of the spaces of physical states of noncritical (anomalous) massive string models can be consistently defined. The appropriate anomalous complexes are obtained by canonical restrictions of the ghost extended spaces to the kernel of curvature operator and additional Gupta-Bleuler-like conditions without any modifications of the matter sector. The cohomologies of the polarized anomalous complex are calculated and analyzed in detail.

Light-cone formulation and spin spectrum of non-critical fermionic string

A free fermionic string quantum model is constructed directly in the light-cone variables in the range of dimensions 1<d<10. It is shown that after the GSO projection this model is equivalent to the fermionic massive string and to the non-critical Ramond-Neveu-Schwarz string. The spin spectrum of the model is analysed. For d=4 the character generating functions is obtained and the particle content of first few levels is numerically calculated.

On parallelizable spheres, division algebras and Clifford algebras

Abstract Exceptionality of S 1 , S 3 , S 7 parallelizable spheres is interrelated not only with division algebras but also with C (0, n ), n =1,3,7 Clifford algebras. The point of view proposed essentially relies on vector-pinor reciprocity.

Fourfold gradings of superalgebras and structures equations describing extended superspaces

Abstract We show how to construct Z2 × Z2 and Z4 gradings of a large class of superalgebras. The classification of such gradings for d = 4, d = 5 and d = 7 anti-de Sitter extended superalgebras is given. It is also shown how the fourfold gradings determine the supersymmetric unification of two bosonic geometries, describing space-time and internal degrees of freedom.