Penrose limits of Abelian and non-Abelian T-duals of $AdS_5\times S^5$ and their field theory duals

We consider the backgrounds obtained by Abelian and non-Abelian T-duality applied on AdS$_{5}$ × S$^{5}$. We study geodesics, calculate Penrose limits and find the associated plane-wave geometries. We quantise the weakly coupled type-IIA string theory on these backgrounds. We study the BMN sector, finding operators that wrap the original quiver CFT. For the non-Abelian plane wave, we find a ‘flow’ in the frequencies. We report some progress to understand this, in terms of deconstruction of a higher dimensional field theory. We explore a relation with the plane-wave limit of the Janus solution, which we also provide.