Adinkras: A graphical technology for supersymmetric representation theory

We present a symbolic method for organizing the representation theory of one-dimensional superalgebras. This relies on special objects, which we have called adinkra symbols, which supply tangible geometric forms to the still-emerging mathematical basis underlying supersymmetry.

Figure 1

Each supersymmetric quantum field theory has a shadow in supersymmetric quantum mechanics obtained by dimensionally reducing all of the spatial dimensions in the field theory.

Figure 2

The root tree for the case $N=1$.

Figure 3

The root tree for the case $N=2$.

Figure 4

The root tree for the case $N=3$.

Figure 5

The $N=4$ root tree.