Non-linear realization of ℵ0-extended supersymmetry

As generalizations of the original Volkov-Akulov action in four-dimensions, actions are found for all space-time dimensions D invariant under N non-linear realized global supersymmetries. We also give other such actions invariant under the global non-linear supersymmetry. As an interesting consequence, we find a non-linear supersymmetric Born-Infeld action for a non-Abelian gauge group For arbitrary D and N, which coincides with the linearly supersymmetric Born-Infeld action in D = 10 at the lowest order. For the gauge group U(N) for M(atrix)-theory, this model has N-2-extended non-linear supersymmetries, so that its large N limit corresponds to the infinitely many (N-0) supersymmetries. We also perform a duality transformation from F-mu nu, into its Hedge dual Nmu 1 ...mu D-2, We next point out that any Chern-Simons action for any (super)groups has the nonlinear supersymmetry as a hidden symmetry. Subsequently, we present a superspace formulation for the component results. We further find that as long as superspace supergravity is consistent, this generalized Volkov-Akulov action can further accommodate such curved superspace backgrounds with local supersymmetry, as a super p-brane action with fermionic kappa-symmetry. We further elaborate these results to what we call "simplified" (Supersymmetry)(2)-models, with both linear and non-linear representations of supersymmetries in superspace at the same time. Our result gives a proof that there is no restriction on D or N for global non-linear supersymmetry. We also see that the non-linear realization of supersymmetry in "curved" space-time can be interpreted as "non-perturbative" effect starting with the "flat" space-time. (C) 2000 Elsevier Science B.V. All rights reserved.