Abstract
Attention is called to an interesting property of the space of one-particle states in some especially important massless field theories: the appearance of a one-particle ghost with zero energy. It appears in conformal as well as de Sitter electrodynamics, in the physical sectors of the field mode representations of the respective symmetry groups. It appears again in super de Sitter electrodynamics based on the superalgebra osp(4/l) and in super conformal electrodynamics based on su(2,2/l). We next construct two families of extended super QED, incorporating this property, based on osp(4/N) and on su(2,2/N). There is precisely one osp(4/N) theory and one su(2,2/N) theory of this type for each value of N. The osp(4/6) theory is the same as N = 6 extended supergravity, this is the only one among this family of osp(4/N) theories in which the highest spin is 2. All the one particle states are massless, and in the osp(4/N) theories they can be interpreted as states of two colored singletons. We also critically examine the concept of the Witten index in flat space as well as in de Sitter supersymmetric field theories.
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Flato, M., Fronsdal, C. (1986). Spontaneously Generated Field Theories, Zero-Center Modules, Colored Singletons and the Virtues of N = 6 Supergravity. In: Fronsdal, C. (eds) Essays on Supersymmetry. Mathematical Physics Studies, vol 8. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-4624-8_4
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DOI: https://doi.org/10.1007/978-94-009-4624-8_4
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