Advances in Theoretical and Mathematical Physics

Volume 15 (2011)

Number 6

Codes and supersymmetry in one dimension

Pages: 1909 – 1970



Charles F. Doran (Department of Mathematical and Statistical Sciences, University of Alberta)

Michael G. Faux (Department of Physics, State University of New York, Oneonta)

Sylvester James, Jr. Gates (Center for String and Particle Theory, University of Maryland, College Park)

Tristan Hübsch (Department of Physics and Astronomy, Howard University)

Kevin M. Iga (Natural Science Division, Pepperdine University)

Gregory D. Landweber (Mathematics Program, Bard College, Annandale-on-Hudson)

Robert L. Miller (Department of Mathematics, University of Washington, Seattle)


\begin{abstract}Adinkras are diagrams that describe many usefulsupermultiplets in $D=1$ dimensions. We show that thetopology of the Adinkra is uniquely determined by a doublyeven code. Conversely, every doubly even code produces apossible topology of an Adinkra. A computation of doublyeven codes results in an enumeration of these Adinkratopologies up to $N=28$, and for minimal supermultiplets,up to $N=32$.

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