Theories with Memory

TL;DR

This paper demonstrates how superspace techniques can reconstruct higher-dimensional supersymmetric theories from their lower-dimensional reductions, exemplified by restoring 4D N=4 Yang-Mills to 6D N=(1,1) Yang-Mills.

Contribution

It introduces a superspace framework that preserves the 'memory' of higher dimensions, enabling the reconstruction of original theories from reduced models.

Findings

Successfully restored 4D N=4 Yang-Mills to 6D N=(1,1) Yang-Mills

Developed supersymmetric truncation within this framework

Worked in light-cone superspace focusing on physical degrees of freedom

Abstract

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.