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We establish results similar to Kramers and Lieb-Schultz-Mattis theorems butinvolving only translation symmetry and for Majorana modes. In particular, weshow that all states are at least doubly degenerate in any one and twodimensional array of Majorana modes with translation symmetry, periodicboundary conditions, and an odd number of modes per unit cell. Moreover, weshow that all such systems have an underlying $\mathcal{N}=2$ supersymmetry andexplicitly construct the generator of the supersymmetry. Furthermore, weestablish that there cannot be a unique gapped ground state in such onedimensional systems with anti-periodic boundary conditions. These generalresults are fundamentally a consequence of the fact that translations forMajorana modes are represented projectively, which in turn stems from theanomalous nature of a single Majorana mode. An experimental signature of thedegeneracy arising from supersymmetry is a zero-bias peak in tunnelingconductance.

All Majorana Models with Translation Symmetry are Supersymmetric