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Supersymmetric (SUSY) models and dynamical breaking of symmetries have been used to explain hierarchies of mass scales. We find that a chiral representation, $overline{bf 10}, oplus, overline{bf 5}, oplus, 2cdot{bf 5}$ in SUSY SU(5) in the hidden sector, breaks global SUSY dynamically, by producing a composite field $phi$ below the SU(5) confinement scale. This dynamincal SUSY breaking can have two important applications, one in particle physics and the other in cosmology. Gavitational effects transmit this dynamical breaking to the standard model(SM) superpartners and the quintessential vacuum energy. The SM superpartners feel the effects just by the magnitude of the gravitino mass while the smallness of the quintessential vacuum energy is due to the composite nature of a singlet field $phi$. The composite $phi$ carries a global charge which is hardly broken in SUSY and hence its phase can be used toward a quintessential axion for dark energy of the Universe.
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In this letter we would like to apply the superconformal index technique to give one more evidence for the theory proposed by Intriligator, Seiberg and Shenker (ISS) as being described by interacting conformal field theory in its IR fixed point.
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We propose a new mechanism of spontaneous supersymmetry breaking. The existence of extra dimensions with nontrivial topology plays an important role. We investigate new features resulted from the mechanism in two simple supersymmetric Z_2 and U(1) models. One of remarkable features is that there exists a phase in which the translational invariance for the compactified directions is broken spontaneously, accompanying the breakdown of the supersymmetry. The mass spectrum of the models appeared in reduced dimensions is a full of variety, reflecting the highly nontrivial vacuum structure of the models. The Nambu-Goldstone bosons (fermions) associated with breakdown of symmetries are found in the mass spectrum. Our mechanism also yields quite different vacuum structures if models have different global symmetries.
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