Quaternionic structures, supertwistors and fundamental superspaces

DIEGO JULIO CIRILO; V. N. PERVUSHIN

INTERNATIONAL JOURNAL OF GEOMETRIC METHODS IN MODERN PHYSICS

WORLD SCIENTIFIC PUBL CO PTE LTD

Lugar: London, UK; Año: 2016

0219-8878

Superspace is considered as space of parameters of the supercoherent states defining the basis for oscillator-like unitary irreducible representations of the generalized superconformal group SU(2m,2n|2N)SU(2m,2n|2N) in the field of quaternions Hℍ. The specific construction contains naturally the supertwistor one of the previous work by Litov and Pervushin [1] and it is shown that in the case of extended supersymmetry such an approach leads to the separation of a class of superspaces and its groups of motion. We briefly discuss this particular extension to the domain of quaternionic superspaces as nonlinear realization of some kind of the affine and the superconformal groups with the final end to include also the gravitational field [6] (this last possibility to include gravitation, can be realized on the basis of Ref. 12 where the coset Sp(8)SL(4R)∼Sp(8)SL(4R)∼SU(2,2)SL(2C)SU(2,2)SL(2C) was used in the non supersymmetric case). It is shown that this quaternionic construction avoid some unconsistencies appearing at the level of the generators of the superalgebras (for specific values of pp and qq; p+q=Np+q=N) in the twistor one.