This paper shows that the positive-energy and non-renormalization theorems of
traditional supersymmetry survive the addition of Lorentz violating
interactions. The Lorentz-violating coupling constants in theories using the
construction of Berger and Kostelecky must obey certain constraints in order to
preserve the positive energy theorem. Seiberg's holomorphic arguments are used
to prove that the superpotential remains non-renormalized (perturbatively) in
the presence of Lorentz-violating interactions of the Berger-Kostelecky type.
We briefly comment on Lorentz-violating theories of the type constructed by
Nibbelink and Pospelov to note that holomorphy arguments offer elegant proofs
of many non-renormalization results, some known by other arguments, some new.Comment: v3: Discussion and clarification added. References added. Results on
gauge-kinetic function expande