Adinkra Isomorphisms and `Seeing' Shapes with Eigenvalues

We create an algorithm to determine whether any two graphical representations (adinkras) of equations possessing the property of supersymmetry in one or two dimensions are isomorphic in shape. The algorithm is based on the determinant of `permutation matrices' that are defined in this work and derivable for any adinkra.Comment: LaTeX twice, 23 pages, 7 figure

On 4D, N = 1 Massless Gauge Superfields of Higher Superspin: Integer Case

We present an alternative method of exploring the component structure of an integer super-helicity Y=s (for any integers) irreducible representation of the Super-Poincare group. We use it to derive the component action and the SUSY transformation laws. The effectiveness of this approach is based on the equations of motion and their properties, like Bianchi identities. These equations are generated by the superspace action when it is expressed in terms of prepotentials. For that reason we reproduce the superspace action for integer superspin, using unconstrained superfields. The appropriate, to use, superfields are dictated by the representation theory of the group and the requirement that there is a smooth limit between the massive and massless case.Comment: LaTeX twice, 23 pp

Progress on cubic interactions of arbitrary superspin supermultiplets via gauge invariant supercurrents

We consider cubic interactions of the form $s-Y-Y$ between a massless integer superspin $s$ supermultiplet and two massless arbitrary integer or half integer superspin $Y$ supermultiplets. We focus on non-minimal interactions generated by gauge invariant supercurrent multiplets which are bilinear in the superfield strength of the superspin $Y$ supermultiplet. We find two types of consistent supercurrents. The first one corresponds to conformal integer superspin $s$ supermultiplets, exist only for even values of $s, s=2\ell+2$, for arbitrary values of $Y$ and it is unique. The second one, corresponds to Poincar\'e integer superspin $s$ supermultiplets, exist for arbitrary values of $s$ and $Y$

A Theory of Spinning Particles for Large N-extended Supersymmetry

An explicit construction of theories of spinning particles, both massive and massless, is given with arbitrary extended supersymmetry on the world-line. As an application of our results, we give a universal description of 3D (and via truncation all lower dimensional) supersymmetric scalar multiplets with arbitrary N-extended supersymmetry.Comment: 11 pages, Latex fil

Minimal Superspace Vector Fields for 5D Minimal Supersymmetry

We investigate a minimal superspace description for 5D superconformal Killing vectors. The vielbein appropriate for AdS symmetry is discussed within the confines of this minimal supergeometry.Comment: 10 page

SUSY Equation Topology, Zonohedra, and the Search for Alternate Off-Shell Adinkras

Results are given from a search to form adinkra-like equations based on topologies that are not hypercubes. An alternate class of zonohedra topologies are used to construct adinkra-like graphs. In particular, the rhombic dodecahedron and rhombic icosahedron are studied in detail. Using these topological skeletons, equations similar to those of a supersymmetric system are found. But these fail to have the interpretation of an off-shell supersymmetric system of equations.Comment: 29 pages, 4 figure

On 4D, N = 1 Massless Gauge Superfields of Higher Superspin: Half-Odd-Integer Case

We present an alternative method to explore the off-shell component structure of theories that describe half-integer super-helicities Y=s+1/2 (where sis any positive integer). We use it to derive the component action, component SUSY transformation laws, and count the component-level degrees of freedom involved. This counting will give us clues about N=2 representations. The foundation of the process relies on the superfield equations of motion, generated by variation of a superspace action expressed in terms of prepotentials. Using this approach we reproduce the half-integer super-helicity superspace action using unconstrained superfields.Comment: LaTeX twice, 31 pp

A Codicil To Massless Gauge Superfields of Higher Integer Superspins

We study theories of 4D, N=1 supersymmetric massless, arbitrary integer superspins. A new state-of-the art is being established by the discovery of a new series of such theories for arbitrary superspin Y (Y=s for any integer s) The lowest member of the series is surprisingly found to be a previously established formulation of the spin (3/2, 1) supermultiplet

A Dynamical Theory for Massive Supergravity

We present a new massive theory of superspin Y=3/2 which has non-minimal supergravity as it's massless limit. The new result will illuminate the underlying structure of auxiliary fields required for the description of arbitrary massive half-integer superspin systems.Comment: LaTeX twice, 12 ppg, 1 figur

A Truly Crazy Idea About Type-IIB Supergravity and Heterotic Sigma-Models

We construct an explicit and manifestly (1,0) heterotic sigma-model where the background fields are those of 10D, N=IIB supergravity.Comment: 10 Pages, Latex (self contained macros