Supersymmetric solutions of type-II supergravity from $\lambda$-deformations and zoom-in limits

We construct the embedding of the $\lambda$-model on $SL(2,\mathbb{R})\times SU(2)\times SU(2)$ in type-II supergravity. In the absence of deformation, the ten-dimensional background corresponds to the near-horizon limit of the NS1-NS5-NS5 brane intersection. We show that when the deformation is turned on, supersymmetry breaks by half, and the solution preserves 8 supercharges. The Penrose limits along two null geodesics of the deformed geometry are also considered. It turns out that none of the associated plane-wave backgrounds exhibit supernumerary supercharges.