Adinkra symbols (physics)
In supergravity and supersymmetric representation theory, Adinkra symbols are a graphical representation of supersymmetric algebras. Mathematically they can be described as colored finite connected simple graphs, that are bipartite and n-regular. Their name is derived from Ashanti symbols of the same name.
One approach to the representation theory of super Lie algebras is to restrict attention to representations in one space-time dimension and having supersymmetry generators, i.e., to superalgebras. In that case, the defining algebraic relationship among the supersymmetry generators reduces to
Here denotes partial differentiation along the single space-time coordinate. One simple realization of the algebra consists of a single bosonic field , a fermionic field , and a generator which acts as
Since we have just one supersymmetry generator in this case, the superalgebra relation reduces to , which is clearly satisfied.
- Faux, M.; Gates, S. J. (2005). "Adinkras: A graphical technology for supersymmetric representation theory". Physical Review D. 71 (6). arXiv:hep-th/0408004. Bibcode:2005PhRvD..71f5002F. doi:10.1103/PhysRevD.71.065002.
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