  We study the Penrose limit of Type IIB duals of softly broken N=1 SU(N) gauge
theories in four dimensions, obtained as deformations of the Maldacena-Nunez
and Klebanov-Strassler backgrounds. We extract the string spectrum on the
resulting pp-wave backgrounds and discuss some properties of the conjectured
dual gauge theory hadrons, the so called "Annulons". The string zero-point
energy on the light-cone is nontrivial, due to the loss of linearly realized
worldsheet supersymmetry, and negative, even in the unbroken supersymmetric
case. This causes the appearance of non-perturbative corrections to the
hadronic mass spectrum. We briefly discuss the thermodynamic behavior of these
string models, calculating the corresponding Hagedorn temperatures.
