N=3 supersymmetric Born-Infeld theory

We construct an off-shell N = 3 supersymmetric extension of the abelian D = 4 Born-Infeld action starting from the action of supersymmetric Maxwell th eory in N = 3 harmonic superspace. A crucial new feature of the N = 3 super BI action is that its interaction part contains only terms of the order 4k in the N = 3 superfield strengths. The correct component bosonic BI action arises as the result of elimination of auxiliary tensor field which is pre sent in the off-shell N = 3 vector multiplet in parallel with the gauge fie ld strength. In this new Legendre-type representation, the bosonic BI actio n is fully specified by a real function of the single variable quartic in t he auxiliary tensor field. The generic choice of this function amounts to a wide set of self-dual nonlinear extensions of the Maxwell action. All of t hem admit an off-shell N = 3 supersymmetrization. (C) 2001 Elsevier Science B.V. All rights reserved.