Saitama Institute of Technology
Okabe-machi, Saitama 369-0293, Japan
E-mail:   shima@sit.ac.jp

Geometry of Nonlinear Supersymmetry in Curved Space-time and Unity of Nature

[The contents are partly published in
Europ. Phys. J., C7, 341 (1999),
Phys. Lett. B 501, 232, (2001),
Phys. Lett. B 507, 260 (2001)].

Abstract:
A unified description of spacetime and matter is proposed by using a single irreducible representation of SO(10) Super-Poincar'e algebra (SO(10)SPA). All (observed) elementary particles except the graviton are the (massless) eigenstates of SO10)SPA composed of fundamental Nambu-Goldstone fermions with spin 1/2, superons, associating with the spontaneous breakdown of the supertranslation of the spacetime. The systematic investigations of the standard model(SM) and SU(5)GUT by using superon diagrams may reveal the three-generations structure, the stability of the proton, the neutral K-, B- and D- mixings, CP-violation, the atmospher and solar neutrino deficits and the absence of the electroweak lepton-flavor-mixing. The fundamental action of the superon-graviton model (SGM) for space-time and matte is proposed, which is an analogue of Einstein-Hilbert action and invariant under a new supersymmetry.
The spacetime symmetries of SGM action proposed as the gravitational coupling of N-G fermions are investigated further. The commutators of new nonlinear supersymmetry (NL SUSY) transformations form a closed algebra, which reveals N-G fermion (NL SUSY) nature and a generlized general coordinate transformation. A generalized local Lorentz transformation, which forms a closed algebra, is also introduced. The structures of SGM action are discussed in some detail.