Theories with Memory

Dimensionally reduced supersymmetric theories retain a great deal of information regarding their higher dimensional origins. In superspace, this "memory" allows us to restore the action governing a reduced theory to that describing its higher-dimensional progenitor. We illustrate this by restoring four-dimensional N=4 Yang-Mills to its six-dimensional parent, N=(1,1) Yang-Mills. Supersymmetric truncation is introduced into this framework and used to obtain the N=1 action in six dimensions. We work in light-cone superspace, dealing exclusively with physical degrees of freedom.