New Goldstone multiplet for partially broken supersymmetry

The partial spontaneous breaking of rigid $N=2\mathrm{}$ supersymmetry implies the existence of a massless $N=1\mathrm{}$ Goldstone multiplet. In this paper we show that the spin-$\mathrm{}(1/2,1)\mathrm{}$ Maxwell multiplet can play this role. We construct its full nonlinear transformation law and find the invariant Goldstone action. The spin-$1$ piece of the action turns out to be of Born-Infeld-type, and the full superfield action is duality invariant. This leads us to conclude that the Goldstone multiplet can be associated with a D-brane solution of superstring theory for $p=3\mathrm{}$. In addition, we find that $N=1\mathrm{}$ chirality is preserved in the presence of the Goldstone-Maxwell multiplet. This allows us to couple it to $N=1\mathrm{}$ chiral and gauge field multiplets. We find that arbitrary Kähler and superpotentials are consistent with partially broken $N=2\mathrm{}$ supersymmetry.