  We present a new class of "dielectric" N=1 supersymmetric solutions of IIB
supergravity. This class contains not just the ten-dimensional lift of the
Leigh-Strassler renormalization group flow, but also the Coulomb branch
deformation of this flow in which the branes are allowed to spread in a
radially symmetric manner, preserving the SU(2) global symmetry. We use the
"algebraic Killing spinor" technique, illustrating how it can be adapted to N=1
supersymmetric flows.
