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Vector Superfields and Lorentz Violation

We extend Lorentz-violating Supersymmetry models to include vector superfields. The CPT-preserving model generalizes easily, while the obvious attempt at generalizing the CPT-violating model meets serious obstructions. Generalizations of the CPT-preserving but Lorentz-Violating model to higher dimensions are also straightforward. Compactification is used to reduce the six-dimensional theory to an ${\cal{N}} =2$ Lorentz-violating theory in four dimensions, while the ten-dimensional theory is used to produce an ${\cal{N}}=4$ Lorentz-violating theory. This may be useful in future constructions involving Ads/CFT correspondence with Lorentz violation.