Adinkra symbols (physics)

In supergravity theory 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 (Adinkra).

One approach to the representation theory of super Lie algebras is to restrict attention to representations in one space-time dimension and having ${\displaystyle N}$ supersymmetry generators, i.e., to ${\displaystyle (1|N)}$ superalgebras. In that case, the defining algebraic relationship among the supersymmetry generators reduces to

Here ${\displaystyle \partial _{\tau }}$ denotes partial differentiation along the single space-time coordinate. One simple realization of the ${\displaystyle (1|1)}$ algebra consists of a single bosonic field ${\displaystyle \phi }$, a fermionic field ${\displaystyle \psi }$, and a generator ${\displaystyle Q}$ which acts as

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