Component on-shell actions of supersymmetric 3-branes II. 3-brane in D=8

TL;DR

This paper constructs the explicit on-shell supersymmetric component action for a 3-brane in D=8, utilizing nonlinear realizations, revealing a structure where higher-order fermionic terms are embedded in covariant derivatives, and fixing parameters through supersymmetry.

Contribution

It provides the first explicit construction of the supersymmetric 3-brane action in D=8 with partial supersymmetry breaking using nonlinear realizations.

Findings

Component action exhibits N=4, d=4 supersymmetry partially broken to N=2, d=4.

Higher-order fermionic terms are incorporated via covariant derivatives and vielbeins.

Parameters in the action are fixed by unbroken supersymmetry.

Abstract

In the present paper we explicitly construct the on-shell supersymmetric component action for a 3-brane moving in D=8 within the nonlinear realizations framework. Similarly to the previously considered case of the super 3-brane in D=6, all ingredients entering the component action follow from the nonlinear realizations approach. The component action of the 3-brane possesses N=4, d=4 supersymmetry partially broken to N=2, d=4 one. The basic Goldstone superfield is the generalized version of N=2,d=4 hypermultiplet. The action has a structure, such that all terms of higher orders in the fermions are hidden inside the covariant derivatives and vielbeins. The main part of the component action mimics its bosonic cousin in which the ordinary space-time derivatives and the bosonic worldvolume are replaced by their covariant (with respect to broken supersymmetry) supersymmetric analogs. The spontaneously broken supersymmetry fixes the Ansatz for the component action, up to two constant parameters. The role of the unbroken supersymmetry is just to fix these parameters.