On dual 3 - brane actions with partially broken N = 2 supersymmetry

The N = 1 superspace generalization of the 3-brane action in 6 dimensions with partially broken N = 2 supersymmetry can be constructed using N = 1 chiral, complex linear, or real linear superfields. The physical scalars of these multiplets give equivalent descriptions of the two transverse coordinates. The second supersymmetry is realized nonlinearly in all these actions. We derive the superspace brane actions and their nonlinear supersymmetry for both kinds of linear superfields when we break N = 2 supersymmetry spontaneously. This breaking is realized in the free action of hypermultiplets that live in N = 2 projective superspace by constraining the N = 2 multiplets to reduce them to a pure Goldstone mul-tiplet. For the chiral superfield, the superspace brane action and nonlinear supersymmetry can be deduced by dualizing the brane action of either linear superfield. We find that the dual action is unique up to field redefinitions that introduce arbitrariness in the dependence on the auxiliary fields.