Related papers: Frames for supersymmetry
We present a symbolic method for organizing the representation theory of one-dimensional superalgebras. This relies on special objects, which we have called adinkra symbols, which supply tangible geometric forms to the still-emerging…
In this paper we discuss off-shell representations of N-extended supersymmetry in one dimension, ie, N-extended supersymmetric quantum mechanics, and following earlier work on the subject codify them in terms of certain graphs, called…
The off-shell representation theory of 4D, $\mathcal{N}=1$ supermultiplets can be categorized in terms of distinct irreducible graphical representations called adinkras as part of a larger effort we call supersymmetry `genomics.' Recent…
There exist myriads of off-shell worldline supermultiplets for (N{\leq}32)-extended supersymmetry in which every supercharge maps a component field to precisely one other component field or its derivative. A subset of these extends to…
We survey the combinatorics of the Adinkra, a graphical device for solving differential equations in supersymmetry. These graphs represent an exceptional class of 1-factorizations with further augmentations. As a new feature, we…
Adinkras are graphical tools created for the study of representations in supersymmetry. Besides having inherent interest for physicists, adinkras offer many easy-to-state and accessible mathematical problems of algebraic, combinatorial, and…
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.
Recent efforts to classify representations of supersymmetry with no central charge have focused on supermultiplets that are aptly depicted by Adinkras, wherein every supersymmetry generator transforms each component field into precisely one…
We explain how all information about ambient component field spin assignments in higher-dimensional off-shell supersymmetry is accessibly coded in one-dimensional restrictions, known as shadows. We also explain how to determine whether the…
We explain how the representation theory associated with supersymmetry in diverse dimensions is encoded within the representation theory of supersymmetry in one time-like dimension. This is enabled by algebraic criteria, derived, exhibited,…
Every finite-dimensional unitary representation of the N-extended worldline supersymmetry without central charges may be obtained by a sequence of differential transformations from a direct sum of minimal Adinkras, simple supermultiplets…
Starting from higher dimensional adinkras constructed with nodes referenced by Dynkin Labels, we define "adynkras." These suggest a computationally direct way to describe the component fields contained within supermultiplets in all…
Adinkras are a graphical tool for studying off-shell representations of supersymmetry. In this paper we efficiently classify the automorphism groups of Adinkras relative to a set of local parameters. Using this, we classify Adinkras…
We introduce a framework for designing multi-scale, adaptive, shift-invariant frames and bi-frames for representing signals. The new framework, called AdaFrame, improves over dictionary learning-based techniques in terms of computational…
A finite-dimensional Hilbert space is usually described in terms of an orthonormal basis, but in certain approaches or applications a description in terms of a finite overcomplete system of vectors, called a finite tight frame, may offer…
Recent work on classicication of off-shell representations of N-extended worldline supersymmetry without central charges has uncovered an unexpectedly vast number--trillions of even just (chromo)topology types--of so called adinkraic…
An introductory theory of frames on finite dimensional quaternion Hilbert spaces is demonstrated along the lines of their complex counterpart.
We demonstrate a method for describing one-dimensional N-extended supermultiplets and building supersymmetric actions in terms of unconstrained prepotential superfields, explicitly working with the Scalar supermultiplet. The method uses…
We construct new families of deformed supersymmetric field theories which break space-time symmetries but preserve half of the original supersymmetry. We do this by writing deformations as couplings to background multiplets. In many cases…
Symmetries impose structure on the Hilbert space of a quantum mechanical model. The mathematical units of this structure are the irreducible representations of symmetry groups and I consider how they function as conceptual units of…