Composite supersymmetric axion-dilaton-dilatino system and the breaking of supersymmetry.

The spontaneous breakdown of the scale, the chiral and the superconformal symmetries for a hidden SU (N) gauge group is studied in an effective lagrangean approach. The relevant low-energy degrees of freedom are taken to be the composite Goldstone particles associated with these three broken symmetries. Super-symmetry is spontaneously broken in the large N limit and soft breaking terms in the observable sector are generated, together with nonrenormalisable Nambu-Jona-Lasinio type interactions. The dilaton and the axion were introduced in field theory for a priori two very different reasons. The axion was first postulated to exist by Weinberg and Wilzcek [1] in order to solve the famous U (1) problem in QCD and is usually seen as the Goldstone boson of the U (1) Peccei-Quinn type symmetries [1] which allow us to dynamically set θ QCD = 0 by a chiral rotation. Its mass and couplings have been extensively studied [2] and the experimental searches impose a rather strong constraint on the scale Λ associated with the spontaneous breakdown of the U (1) symmetry 10 8 GeV < Λ < 10 12 GeV. To obtain such values in a natural way (avoiding a new hierarchy problem) the composite models of axions [3] seem to be the most simple and elegant. A new gauge group is introduced with the corresponding coupling constant becoming strong at the scale Λ producing fermion condensation and the breaking of the Peccei-Quinn symmetry. These models need new exotic coloured fermions whose only manifestation at low energies is through the composite axion. The dilaton was originally introduced with the hope of understanding the cosmological constant problem, i.e. why the cosmological constant postulated by Einstein in the general relativity field equations is so small [4]. Even if it fails in this respect it has remarkable properties worth to be studied. At the classical level it restores the dilatation invariance and is the Goldstone boson associated with the spontaneaous breakdown of this symmetry. In a supersymmetric theory the two symmetries seem to be very close in the sense that the corresponding improved currents, together with the supersymmetry current transform into themselves under supersymmetry and form a realsupermul-tiplet of currents [5]. The corresponding charges together with Poincaré, supersymmetry and con-formal generators give rise to the superconformal algebra [6]. Classically the su-perconformal group is a symmetry in the limit of zero masses and is plagued with quantum anomalies [7]. Introducing a common …