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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.
Representations of four-dimensional superconformal groups on harmonic superfields are discussed. It is argued that any representation can be given as a superfield on many superflag manifolds. Representations on analytic superspaces do not require con
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
Representations of four-dimensional superconformal groups on harmonic superfields are discussed. It is shown how various short representations can be obtained by parabolic induction. It is also shown that such short multiplets may admit several descr
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.
We compute the partition functions of D(-1)D7 systems describing the multi-instanton dynamics of SO(N) gauge theories in eight dimensions. This is the simplest instance of the so called exotic instantons. In analogy with the Seiberg-Witten theory in