  We study semiclassical strings in the Klebanov-Witten and in the Non-abelian
T-dual Klebanov-Witten backgrounds. We show that both backgrounds share a
subsector of equivalent states up to conditions on the T-dual coordinates which
also impose a breaking of the R-symmetry by a discrete group. We also analyze
string configurations where the strings are stretched along the T-dual
coordinates. This semiclassical analysis predicts the existence of chiral
primary operators for the dual (strongly coupled) superconformal field theory
whose anomalous dimension depends on the T-dual coordinates. We briefly discuss
the Penrose limit of the dualised background.
