Structural Theory of 2-d Adinkras
@article{Iga2015StructuralTO, title={Structural Theory of 2-d Adinkras}, author={Kevin Iga and Yan X. Zhang}, journal={arXiv: High Energy Physics - Theory}, year={2015} }
Adinkras are combinatorial objects developed to study (1-dimensional) supersymmetry representations. Recently, 2-d Adinkras have been developed to study 2-dimensional supersymmetry. In this paper, we classify all 2-d Adinkras, confirming a conjecture of T. Hubsch. Along the way, we obtain other structural results, including a simple characterization of Hubsch’s even-split doubly even codes.
6 Citations
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Adinkra height yielding matrix numbers: Eigenvalue equivalence classes for minimal four-color adinkras
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An adinkra is a graph-theoretic representation of space–time supersymmetry. Minimal four-color valise adinkras have been extensively studied due to their relations to minimal 4D, [Formula: see text]…
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A bstractWe present an expanded and detailed discussion of the mathematical tools required to cull and filter representations of the Coxeter Group BC4 into providing bases for the construction of…
Properties of HYMNs in examples of four-color, five-color, and six-color adinkras
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The mathematical concept of a "Banchoff index" associated with discrete Morse functions for oriented triangular meshes has been shown to correspond to the height assignments of nodes in adinkras. In…
References
SHOWING 1-10 OF 16 REFERENCES
Codes and supersymmetry in one dimension
- Computer Science
- 2011
It is shown that the topology of the Adinkra is uniquely determined by a doubly even code, which results in an enumeration of these AdinkRA topologies up to N=28, and for minimal supermultiplets, up toN=32.
Topology Types of Adinkras and the Corresponding Representations of N -Extended Supersymmetry
- Computer Science, Mathematics
- 2008
A relationship between Adinkra diagrams and quotients of N-dimensional cubes is demonstrated, and how these quotient groups correspond precisely to doubly even binary linear error-correcting codes provides a means for describing equivalence classes of Adinkras and therefore supermultiplets.
Adinkras for mathematicians
- Mathematics
- 2011
Adinkras are graphical tools created for the study of supersymmetry representations. Besides having in- herent interest for physicists, the study of adinkras has already shown connections with coding…
Automorphism Properties and Classification of Adinkras
- Mathematics
- 2015
Adinkras are graphical tools 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.…
An application of Cubical Cohomology to Adinkras and Supersymmetry Representations
- Mathematics
- 2012
An Adinkra is a class of graphs with certain signs marking its vertices and edges, which encodes off-shell representations of the super Poincar\'e algebra. The markings on the vertices and edges of…
On Graph-Theoretic Identifications of Adinkras, Supersymmetry Representations and Superfields
- Mathematics
- 2007
In this paper, we discuss off-shell representations of N-extended supersymmetry in one dimension, i.e. N-extended supersymmetric quantum mechanics, and following earlier work on the subject, we…
Adinkras: A graphical technology for supersymmetric representation theory
- Mathematics
- 2005
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…
Relating Doubly-Even Error-Correcting Codes, Graphs, and Irreducible Representations of N-Extended Supersymmetry
- Mathematics
- 2008
Previous work has shown that the classification of indecomposable off-shell representations of N-supersymmetry, depicted as Adinkras, may be factored into specifying the topologies available to…
On dimensional extension of supersymmetry: From worldlines to worldsheets
- Mathematics
- 2012
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…