String spectrum of curved string backgrounds obtained by T-duality and   shifts of polar angles
  A class of exactly solvable string models can be obtained by starting with flat space and combining T-duality and shifts of angular coordinates of several polar planes. The models are the analog of the Lunin-Maldacena \beta-deformation of the AdS_5 x S^5 type IIB string background, which is dual to a Leigh-Strassler deformation of \N=4 Super Yang-Mills Theory.   We determine the complete physical string spectrum for two string models obtained in this way, by explicitly solving the string equations and quantizing in terms of free creation and annihilation operators. We also show that the 3-parameter (b_1,b_2,b_3) model, obtained by three independent TsT transformations, has tachyons in some regions of the parameter space. 
Jorge G. Russo