  We establish results similar to Kramers and Lieb-Schultz-Mattis theorems but
involving only translation symmetry and for Majorana modes. In particular, we
show that all states are at least doubly degenerate in any one and two
dimensional array of Majorana modes with translation symmetry, periodic
boundary conditions, and an odd number of modes per unit cell. Moreover, we
show that all such systems have an underlying $\mathcal{N}=2$ supersymmetry and
explicitly construct the generator of the supersymmetry. Furthermore, we
establish that there cannot be a unique gapped ground state in such one
dimensional systems with anti-periodic boundary conditions. These general
results are fundamentally a consequence of the fact that translations for
Majorana modes are represented projectively, which in turn stems from the
anomalous nature of a single Majorana mode. An experimental signature of the
degeneracy arising from supersymmetry is a zero-bias peak in tunneling
conductance.
