Adinkras: A Graphical Technology for Supersymmetric Representation Theory

Abstract

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 mathematical basis underlying supersymmetry.

44 pages, LaTeX, 35 figures

References in corpus (2)

• When Superspace Is Not Enough
• Central Charges and Extra Dimensions in Supersymmetric Quantum Mechanics

Cited by in corpus (84)

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• 4D, N = 1 Supersymmetry Genomics (I)
• Spin Gauge Theory of Gravity in Clifford Space: A Realization of Kaluza-Klein Theory in 4-Dimensional Spacetime
• Refining the classification of the irreps of the 1D N-Extended Supersymmetry
• On Graph-Theoretic Identifications of Adinkras, Supersymmetry Representations and Superfields
• D-module Representations of N=2,4,8 Superconformal Algebras and Their Superconformal Mechanics
• Topology Types of Adinkras and the Corresponding Representations of N-Extended Supersymmetry
• Spin Holography via Dimensional Enhancement
• Relating Doubly-Even Error-Correcting Codes, Graphs, and Irreducible Representations of N-Extended Supersymmetry
• Critical scaling dimension of D-module representations of N=4,7,8 Superconformal Algebras and constraints on Superconformal Mechanics
• On the Matter of N=2 Matter
• Clifford Space as a Generalization of Spacetime: Prospects for QFT of Point Particles and Strings
• N=4, d=1 tensor multiplet and hyper-Kahler sigma-models
• SU(2) reduction in N=4 supersymmetric mechanics
• Decomposition and Oxidation of the N-Extended Supersymmetric Quantum Mechanics Multiplets
• On non-minimal N=4 supermultiplets in 1D and their associated sigma-models
• From worldline to quantum superconformal mechanics with/without oscillatorial terms: $D(2,1;\alpha )$ and $sl(2|1)$ models
• Super-Carrollian and Super-Galilean Field Theories
• Adinkra (In)Equivalence From Coxeter Group Representations: A Case Study
• Weaving Worldsheet Supermultiplets from the Worldlines Within
• Graph Theory and Qubit Information Systems of Extremal Black Branes
• A Journey Through Garden Algebras
• From Diophantus to Supergravity and massless higher spin multiplets
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• The Real Anatomy of Complex Linear Superfields
• Adinkras for Clifford Algebras, and Worldline Supermultiplets
• Adinkras and SUSY Holography
• A Lorentz Covariant Holoraumy-Induced "Gadget" From Minimal Off-Shell 4D, N = 1 Supermultiplets
• 4D, N = 1 Supersymmetry Genomics (II)
• Superfield Formulation of Nonlinear N=4 Supermultiplets
• Adinkras, 0-branes, Holoraumy and the SUSY QFT/QM Correspondence
• Taming the zoo of supersymmetric quantum mechanical models
• Effective Symmetries of the Minimal Supermultiplet of N = 8 Extended Worldline Supersymmetry
• A Superfield for Every Dash-Chromotopology
• On General Off-Shell Representations of Worldline (1D) Supersymmetry
• Pure and entangled N=4 linear supermultiplets and their one-dimensional sigma-models
• Super-Zeeman Embedding Models on N-Supersymmetric World-Lines
• On the Four Dimensional Holoraumy of the 4D, $\mathcal{N}$ = 1 Complex Linear Supermultiplet
• Supersymmetric Extension of Hopf Maps: N=4 sigma-models and the S^3 -> S^2 Fibration
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• The 300 "Correlators" Suggests 4D, $\mathcal{N}$ = 1 SUSY Is a Solution to a Set of Sudoku Puzzles
• Superconformal Quantum Mechanics from M2-branes
• Automorphism Properties of Adinkras
• Golden Ratio Controlled Chaos in Supersymmetric Dynamics
• Is It Possible To Embed A 4D, N = 4 Supersymmetric Vector Multiplet Within A Completely Off-Shell Adinkra Hologram?
• A Q-Continuum of Off-Shell Supermultiplets
• N=4 mechanics with diverse (4,4,0) multiplets: explicit examples of HKT, CKT, and OKT geometries
• Think Different: Applying the Old Macintosh Mantra to the Computability of the SUSY Auxiliary Field Problem
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• Superspace: a Comfortably Vast Algebraic Variety
• Adinkra Height Yielding Matrix Numbers: Eigenvalue Equivalence Classes for Minimal Four-Color Adinkras
• Extended supersymmetry with central charges in Dirac action with curved extra dimensions
• Adinkras From Ordered Quartets of BC4 Coxeter Group Elements and Regarding Another Gadget's 1,358,954,496 Matrix Elements
• The Conformal Hyperplet
• On the Construction and the Structure of Off-Shell Supermultiplet Quotients
• On Alphabetic Presentations of Clifford Algebras and Their Possible Applications
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• Superfield Component Decompositions and the Scan for Prepotential Supermultiplets in 10D Superspaces
• Adinkra Foundation of Component Decomposition and the Scan for Superconformal Multiplets in 11D, N = 1 Superspace
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• Extended supersymmetry with central charges in higher dimensional Dirac action
• Adinkra Isomorphisms and `Seeing' Shapes with Eigenvalues
• Examples of 4D, N = 2 Holoraumy
• Component Decompositions and Adynkra Libraries for Supermultiplets in Lower Dimensional Superspaces
• 4D, $\mathcal{N}=1$ Matter Gravitino Genomics
• On the Ubiquity Of Electromagnetic-Duality Rotations in 4D, N = 1 Holoraumy Tensors for On-Shell 4D Supermultiplets
• N=4, d=1 Supersymmetric Hyper-Kaehler Sigma Models with Isospin Variables
• N=4 and N=8 SUSY Quantum Mechanics and Klein's Vierergruppe
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• Structural Theory of 2-d Adinkras
• On the Road Towards the Quantum Geometer's Universe: An Introduction to Four-Dimensional Supersymmetric Quantum Field Theories
• A Note on the Critical Groups of Strongly Regular Graphs and Their Generalizations
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• SUSY Equation Topology, Zonohedra, and the Search for Alternate Off-Shell Adinkras
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• A Note On Exemplary Off-Shell Constructions Of 4D, $\mathcal{N}$ = 2 Supersymmetry Representations
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