Adinkra symbols (physics)

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

In supergravity theory 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 Ashanti symbols of the same name (Adinkra).[7]

Overview[edit]

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.

References[edit]

  1. ^ Faux, M.; Gates, S. J. (2005). "Adinkras: A graphical technology for supersymmetric representation theory". Physical Review D. 71 (6). arXiv:hep-th/0408004Freely accessible. Bibcode:2005PhRvD..71f5002F. doi:10.1103/PhysRevD.71.065002. 
  2. ^ S. James Gates Jr.: "Superstring Theory: The DNA of Reality Archived September 26, 2007, at the Wayback Machine." (The Teaching Company)
  3. ^ S.J. Gates, Jr.: "Symbols of Power, Physics World, Vol. 23, No 6, June 2010, pp. 34 - 39" Archived July 26, 2011, at the Wayback Machine.
  4. ^ S.J. Gates, Jr.: "Quarks to Cosmos Archived March 19, 2011, at the Wayback Machine."
  5. ^ S.J. Gates, Jr., and T. Hubsch, "On Dimensional Extension of Supersymmetry: From Worldlines to Worldsheets"
  6. ^ http://arxiv.org/pdf/1111.6055.pdf
  7. ^ http://www.onbeing.org/blog/symbols-power-adinkras-and-nature-reality/2438

External links[edit]