Abstract
The first complete and explicit SO(1,9) Lorentz descriptions of all component fields contained in the mathcal{N} = 1, mathcal{N} = 2A, and mathcal{N} = 2B unconstrained scalar 10D superfields are presented. These are made possible by a discovery of the dependence of the superfield component expansion on the branching rules of irreducible representations in one ordinary Lie algebra into one of its Lie subalgebras. Adinkra graphs for ten dimensional superspaces are defined for the first time, whose nodes depict spin bundle representations of SO(1,9). A consequential deliverable of this advance is it provides the first explicit, in terms of component fields, examples of all the off-shell 10D Nordström SG theories relevant to string theory, without off-shell central charges that are reducible but with finite numbers of fields. An analogue of Breitenlohner’s approach is implemented to scan for superfields that contain graviton(s) and gravitino(s), which are the candidates for the superconformal prepotential superfields of 10D off-shell supergravity theories and Yang-Mills theories.
Highlights
On the basis of superspace geometry, recently a study [1] of the problem of describing scalar gravitation at the linearized level within the context of eleven and ten dimensional superspaces was completed
One of the longest unsolved problems in the study of supersymmetry is the fact that an irreducible off-shell formulation containing a finite number of component fields for the ten dimensional supergravity multiplet has not been presented
An even simpler problem is to give a detailed component level presentation of a reducible off-shell formulation explicitly showing a finite number of component fields
Summary
On the basis of superspace geometry, recently a study [1] of the problem of describing scalar gravitation at the linearized level within the context of eleven and ten dimensional superspaces was completed. In this work we have new developed techniques, both algorithmic and analytical, that allow the first complete and explicit SO(1, 9) Lorentz descriptions of all component fields contained in 10D, N = 1, N = 2A, and N = 2B unconstrained scalar superfields. They form the maximal reducible and relevant supermultiplets. Its complete structure is given in the form of a list of the component field representations it contains
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