Quantum integrability of sigma models on AII and CII symmetric spaces

Exact massive S-matrices for two-dimensional sigma models on symmetric spaces SU(2N)/Sp(N) and Sp(2P)/Sp(P)×Sp(P) are conjectured. They are checked by comparison of perturbative and non-perturbative TBA calculations of free energy in a strong external field. We find the mass spectrum of the models and calculate their exact mass gap.