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We construct a new off-shell $\mathcal{N}{=}4$, $d{=}3$ nonlinear vectorsupermultiplet. The irreducibility constraints for the superfields leave inthis supermultiplet the same component content as in the ordinary linear vectorsupermultiplet. We present the most general sigma-model type action for the$\mathcal{N}{=}4$, $d{=}3$ electrodynamics with the nonlinear vectorsupermultiplet, which despite the nonlinearity of the supermultiplet may bewritten as an integral over a chiral superspace. This action share the mostimportant properties with its linear counterpart. We also perform thedualization of the vector component into a scalar one and find thecorresponding $\mathcal{N}{=}4$, $d{=}3$ supersymmetric action which describesnew hyper-K\"ahler sigma-model in the bosonic sector.Comment: 8 pages, LaTeX file, PACS numbers: 11.30.Pb, 03.65.-

physical review. d. particles, fields, gravitation, and cosmology/physical review. d, particles, fields, gravitation, and cosmology

<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>N</mml:mi><mml:mo>=</mml:mo><mml:mn>4</mml:mn></mml:math>supersymmetric<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>d</mml:mi><mml:mo>=</mml:mo><mml:mn>3</mml:mn></mml:math>nonlinear electrodynamics

N=4supersymmetricd=3nonlinear electrodynamics