  We construct new families of deformed supersymmetric field theories which
break space-time symmetries but preserve half of the original supersymmetry. We
do this by writing deformations as couplings to background multiplets. In many
cases it is important to use the off-shell representation as auxiliary fields
of the non-dynamical fields must be turned on to preserve supersymmetry. We
also consider backgrounds which preserve some superconformal symmetry, finding
scale-invariant field profiles, as well as $\mathcal{N} =2$ theories on $S^3$.
We discuss how this is related to previous work on interface SCFTs and other
holographic calculations.
