Pulsating strings in $Schr_5 times T^{1,1}$ background

The quest for extension of holographic correspondence to non-relativistic sectors naturally includes Schrodinger backgrounds and their field theory duals. In this paper we study the holography by probing the correspondence with pulsating strings. The case we consider is pulsating strings in five-dimensional Schrodinger space times five-torus $T^{1,1}$, which has as field theory dual a dipole CFT. First we find particular pulsating string solutions and then semi-classically quantize the theory. We obtain the wave function of the problem and thoroughly study the corrections to the energy, which by duality are supposed to give anomalous dimensions of certain operators in the dipole CFT.