Abstract
Among the solutions of string theory and supergravity which preserve some fraction of supersymmetry, the best known are those that leave one half of the supersymmetry unbroken, and there is a large number of field theory models with this pattern of supersymmetry breaking. However, a lot of brane configurations exist which preserve only $1/4$, $1/8$ or more exotic fractions of supersymmetry, and field theory side of these systems remains largely unexplored. To find whether the formalism of nonlinear realizations is useful in construction of models of this type, we consider the systems of some $N_0$ scalar and vector $N=1$, $d=3$ Goldstone supermultiplets. We find that it is possible to construct an $SO(N_0)$ invariant theory of $N_0$ scalar multiplets with $N_0$ broken supersymmetries. For $N_0=3$ or $N_0\geq 5$ its action is not of Nambu-Goto type and its structure remains universal for arbitrary $N_0$. The cases of $N_0=1,2$ correspond to the membranes in $D=4$ and $D=5$, respectively, while for $N_0=4$ some arbitrariness in the action remains, and with proper choice of parameters, it is possible to obtain the action of the membrane in $D=7$ in the bosonic limit. It is also shown that the $SO(N_0)$ invariant action of $N_0$ vector multiplets with $1/N_0$ pattern of supersymmetry breaking does not exist for arbitrary $N_0$.
Highlights
Studies of systems with partial spontaneous breaking of global supersymmetry (PBGS) make up an important branch of all supersymmetry studies
Systems with PBGS play an important role in string theory and supergravity where a lot of solutions that satisfy the Bogomol'nyi-PrasadSommerfield (BPS) condition and preserve some fraction of supersymmetry can be found
The best known solutions preserve one half of the supersymmetry and comprise the brane scan [1,2,3]. For many of these solutions (D-branes, p-branes) the effective actions, superfield or component, which can be determined by the invariance with respect to both broken and unbroken supersymmetries, are known
Summary
Studies of systems with partial spontaneous breaking of global supersymmetry (PBGS) make up an important branch of all supersymmetry studies. Solutions were found that preserve the n=32 fraction of supersymmetry, where n 1⁄4 0; 1; 2; 3; 4; 5; 6; 8; 16 (see [4], where the 3=4 fraction was proposed, and references therein) For systems with these patterns of breaking, the effective actions are much less known. The idea of constructing component actions of theories with partial breaking of supersymmetry is related to the fact that one can realize transformations of the superspace coordinates, Goldstone fermions and, optionally, Goldstone bosons by multiplications in some coset space. We do not concentrate on the already known systems of branes with unusual amounts of preserved supersymmetry but study the three-dimensional models with one unbroken N 1⁄4 1 supersymmetry and some N0 number of spontaneously broken supersymmetries, which are realized by the shifts of the Goldstone fermionic fields. Two separate cases can be studied as the Goldstone fermions can belong to either scalar or vector multiplets
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