Component on shell actions of supersymmetric 3-brane I. 3-brane in D=6

TL;DR

This paper constructs the on-shell supersymmetric component action for a 3-brane in six-dimensional space using nonlinear realizations, emphasizing broken supersymmetry and geometric covariant objects.

Contribution

It provides a nearly algorithmic method to derive the supersymmetric 3-brane action in D=6, focusing on broken supersymmetry and geometric covariant formulations.

Findings

Action expressed in terms of covariant vielbeins and derivatives

Higher-order fermion terms hidden in covariant objects

Main action resembles bosonic case with supersymmetric covariantization

Abstract

In the present and accompanying papers we explicitly construct the on-shell supersymmetric component actions for 3-branes moving in D=6 and in D=8 within the nonlinear realizations framework. In the first paper we apply our schema to construct the action of supersymmetric 3-brane in D=6. It turns out that all ingredients entering the component action can be obtained almost algorithmically by using the nonlinear realizations approach. Within this approach, properly adapted to the construction of on-shell component actions, we pay much attention to broken supersymmetry. Doing so, we were able to write the action in terms of purely geometric objects (vielbeins and covariant derivatives of the physical bosonic components), covariant with respect to broken supersymmetry. It turns out that all terms of the higher orders in the fermions, are hidden inside these covariant derivatives and vielbeins. Moreover, the main part of the component action just mimics its bosonic cousin in which the ordinary space-time derivatives and the bosonic world volume are replaced by their covariant supersymmetric analogs. The Wess-Zumino term in the action, which does not exist in the bosonic case, can be also easily constructed in terms of reduced Cartan forms. Keeping the broken supersymmetry almost explicit, one may write the Ansatz for the component action, fully defined up to two constant parameters. The role of the unbroken supersymmetry is just to fix these parameters.