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 $\mathcal{N}=2$ Lorentz-violating theory in four dimensions, while the ten-dimensional theory is used to produce an $\mathcal{N}=4$ Lorentz-violating theory. This may be useful in future constructions involving AdS/CFT correspondence with Lorentz violation.

• Received 8 October 2010

DOI:https://doi.org/10.1103/PhysRevD.83.025021