Partial breaking of arbitrary amount of d=3 supersymmetry

TL;DR

This paper explores the construction of supersymmetric models with arbitrary fractions of broken supersymmetry using nonlinear realizations, revealing universal structures and limitations for different numbers of supermultiplets.

Contribution

It demonstrates the possibility of constructing $SO(N_0)$ invariant theories with $N_0$ broken supersymmetries and identifies cases where the action is of Nambu-Goto type or not.

Findings

Universal structure for $N_0 eq 4$ in scalar multiplet actions.

Membrane actions in $D=4$, $D=5$, and $D=7$ for specific $N_0$ values.

Non-existence of $SO(N_0)$ invariant vector multiplet actions with $1/N_0$ supersymmetry breaking.

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 $N_0$.