Adinkra symbols

A small Adinkra graph.

In supergravity and supersymmetric representation theory, Adinkra symbols are a graphical representation of supersymmetric algebras.[1][2][3][4][5] Mathematically they can be described as colored finite connected simple graphs, that are bipartite and n-regular.[6] Their name is derived from Adinkra symbols of the same name, and they were introduced by Michael Faux and Sylvester James Gates in 2004.[1]

## Contents

* 1 Overview
* 2 See also
* 3 References
* 4 External links

## Overview

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

{QI,QJ}=2iδIJ∂τ.

Here ∂τ denotes partial differentiation along the single space-time coordinate. One simple realization of the (1|1) algebra consists of a single bosonic field ϕ, a fermionic field ψ, and a generator Q which acts as

Qϕ=iψ,
Qψ=∂τϕ.

Since we have just one supersymmetry generator in this case, the superalgebra relation reduces to Q2=i∂τ, which is clearly satisfied. We can represent this algebra graphically using one solid vertex, one hollow vertex, and a single colored edge connecting them.

## See also

* Feynman diagram

## References

1. ↑ 1.0 1.1 Faux, M.; Gates, S. J. (2005). "Adinkras: A graphical technology for supersymmetric representation theory". Physical Review D 71 (6): 065002. doi:10.1103/PhysRevD.71.065002. Bibcode: 2005PhRvD..71f5002F.
2. ↑ S. James Gates Jr.: "Superstring Theory: The DNA of Reality " (The Teaching Company)
3. ↑ S.J. Gates, Jr.: "Symbols of Power, Physics World, Vol. 23, No 6, June 2010, pp. 34 - 39"
4. ↑ S.J. Gates, Jr.: "Quarks to Cosmos "
5. ↑ S.J. Gates, Jr., and T. Hubsch, "On Dimensional Extension of Supersymmetry: From Worldlines to Worldsheets"
6. ↑ Zhang, Yan X. (2011). "Adinkras for Mathematicians". arXiv:1111.6055 [math.CO].

## External links

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

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