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Register a new userComponent Decompositions and Adynkra Libraries for Supermultiplets in Lower Dimensional Superspaces
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We present Adynkra Libraries that can be used to explore the embedding of multiplets of component field (whether on-shell or partial on-shell) within Salam-Strathdee superfields for theories in dimension nine through four.
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The first complete and explicit SO(1,9) Lorentz descriptions of all component fields contained in $mathcal{N} = 1$, $mathcal{N} = 2$A, and $mathcal{N} = 2$B unconstrained scalar 10D superfields are presented. These are made possible by the discovery of the relation of the superfield component expansion as a consequence of 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). An analog of Breitenlohners approach is implemented to scan for superfields that contain graviton(s) and gravitino(s), which are the candidates for the prepotential superfields of 10D off-shell supergravity theories and separately abelian Yang-Mills theories are similarly treated. Version three contains additional content, both historical and conceptual, which broaden the reach of the scan in the 10D Yang-Mills case.
As the full off-shell theories of supergravity in the important dimensions of eleven and ten dimensions are currently unknown, we introduce a superfield formalism as a foundation and experimental laboratory to explore the possibility that the scal
We introduce N-extended (p,q) AdS superspaces in three space-time dimensions, with p+q=N and p>=q, and analyse their geometry. We show that all (p,q) AdS superspaces with X^{IJKL}=0 are conformally flat. Nonlinear sigma-models with (p,q) AdS supersymmetry exist for p+q<=4 (for N>4 the target space geometries are highly restricted). Here we concentrate on studying off-shell N=3 supersymmetric sigma-models in AdS_3. For each of the cases (3,0) and (2,1), we give three different realisations of the supersymmetric action. We show that (3,0) AdS supersymmetry requires the sigma-model to be superconformal, and hence the corresponding target space is a hyperkahler cone. In the case of (2,1) AdS supersymmetry, the sigma-model target space must be a non-compact hyperkahler manifold endowed with a Killing vector field which generates an SO(2) group of rotations of the two-sphere of complex structures.
We present aspects of the component description of linearized Nordstr om Supergravity in eleven and ten dimensions. The presentation includes low order component fields in the supermultiplet, the supersymmetry variations of the scalar graviton and gravitino trace, their supercovariantized field strengths, and the supersymmetry commutator algebra of these theories.
Proposals are made to describe the Weyl scaling transformation laws of supercovariant derivatives $ abla{}_{underline A}$, the torsion supertensors $T{}_{{underline A} , {underline B}}{}^{{underline C}}$, and curvature supertensors $R{}_{{underline A} , {underline B}}{}_{, underline c} {}^{underline d}$ in 10D superspaces. Starting from the proposal that an unconstrained supergravity prepotential for the 11D, $mathcal{N}$ = 1 theory is described by a scalar superfield, considerations for supergravity prepotentials in the 10D theories are enumerated. We derive infinitesimal 10D superspace Weyl transformation laws and discover ten possible 10D, $mathcal{N}$ = 1 superfield supergravity prepotentials. The first identification of all off-shell ten dimensional supergeometrical Weyl field strength tensors, constructed from respective torsions, is presented.
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