Spinning Strings on Deformed AdS_5 x T^{1,1} with NS B-field

We study classical spinning closed string configuration on logarithmically deformed AdS_5 x T^{1,1} background with non-trivial Neveu-Schwarz B-field in which IIB string theory is dual to a non-conformal N=1 SU(N+M) x SU(N) gauge theory. The integrability on original AdS_5 x T^{1,1} background are significantly reduced by B-field. We find several spinning string solutions with two different ansatzs. Solutions for point-like strings and few circular strings are explicitly obtained. Folded spinning string solutions along radial direction are shown to be allowed in this background. These solutions exhibit novel properties and bring some challenges to understand them from dual quantum field theory.