Adinkra symbols (physics)

File:AdinkraGraph.svg

A small adinkra graph, that is graph isomorphic to a cube. (Dashed lines have been omitted)

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 $N$ supersymmetry generators, i.e., to $(1|N)$ superalgebras. In that case, the defining algebraic relationship among the supersymmetry generators reduces to

$\{Q_I, Q_J\} = 2 i \delta _{I J} \partial_\tau$.

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

$Q \phi= i \psi$,

$Q \psi= \partial_\tau \phi$.

External links

• http://golem.ph.utexas.edu/category/2007/08/adinkras.html
• http://www.flickr.com/photos/science_and_thecity/2796684536/
• http://www.flickr.com/photos/science_and_thecity/2795836787/
• http://www.thegreatcourses.com/courses/superstring-theory-the-dna-of-reality.html

• S. James Gates Jr.: "Superstring Theory: The DNA of Reality" (The Teaching Company)
• S.J. Gates, Jr.: "Symbols of Power, Physics World, Vol. 23, No 6, June 2010, pp. 34 - 39"
• S.J. Gates, Jr.: "Quarks to Cosmos"
• S.J. Gates, Jr., and T. Hubsch, "On Dimensional Extension of Supersymmetry: From Worldlines to Worldsheets"
• http://arxiv.org/pdf/1111.6055.pdf
• http://www.onbeing.org/blog/symbols-power-adinkras-and-nature-reality/2438