BRST cohomologies of non-critical RNS strings

The BRST cohomologies of non-critical massive RNS theories are analysed in detail in the range of dimensions 1 < d < 10. It is shown that the spaces o f physical states admit the relative BRST resolutions: the theorems on vani shing of bigraded-Dolbeaut type cohomologies and relative BRST cohomologies are proved. The no-ghost theorem for relative classes guarantees quantum m echanical consistency of these string models. The explicit correspondence b etween relative cohomology states and the physical states of 'old covariant ' formalism is established: a light-cone gauge slice is shown to be a local section of relative cohomologies. The problem of reconstruction of absolut e BRST cohomologies out of those of the relative complex is also explicitly solved.