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Supersymmetric Yang-Mills equations in $$10+2$$ dimensions. (English) Zbl 1017.81514
Summary: We present a model for supersymmetric Yang-Mills theory in $$10+2$$ dimensions. Our construction uses a constant null vector, and leads to a consistent set of field equations and constraints. The model is invariant under generalized translations and an extra gauge transformation. Ordinary dimensional reduction to ten dimensions yields the usual supersymmetric Yang-Mills equations, while dimensional reduction to $$2+2$$ yields supersymmetric Yang-Mills equations in which the Poincaré supersymmetry is reduced by a null vector. We also give the corresponding formulation in superspace.

##### MSC:
 81T60 Supersymmetric field theories in quantum mechanics 81T13 Yang-Mills and other gauge theories in quantum field theory
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