Orbifold symmetry reductions of massive boson-fermion degeneracy

We investigate the existence of string vacua with Massive Spectrum Degeneracy Symmetry (MSDS) in Heterotic and Type II orbifold constructions. We present a classification of all possible Z2N-orbifolds with MSDS symmetry that can be constructed in the formalism of the 2d free fermionic construction. We explicitly construct several two-dimensional models whose Reduced Massive Spectrum Degeneracy Symmetry (RMSDS) is due to a set of Z2-orbifold projections induced naturally in the framework of the free fermionic construction. In all proposed models the massive boson and fermion degrees of freedom exhibit Massive Spectrum Degeneracy Symmetry while the number of massless bosons n(b) and massless fermions n(f) are different; n(b)≠n(f). This property distinguishes the MSDS Z2-twisted theories from ordinary supersymmetric ones. Some comments are stated concerning the large marginal JJ¯-deformations of the proposed models connecting them to higher-dimensional gauged-supergravity theories with non-trivial geometrical fluxes.