Matrix Supermultiplet of N=2, D=4 Supersymmetry and Supersymmetric 3-brane

TL;DR

This paper constructs an infinite-dimensional supermultiplet framework for N=2, D=4 supersymmetry, showing how the supersymmetric 3-brane Lagrangian emerges as a component and deriving the PBGS action.

Contribution

It introduces a novel matrix superfield approach to describe the supersymmetric 3-brane within N=2, D=4 supersymmetry, linking supermultiplet components to brane dynamics.

Findings

Supermultiplet components relate to brane Lagrangian

Solution for V_{11} yields PBGS action

Covariant expression of superfield components

Abstract

It is shown that the Lagrangian density of the supersymmetric 3-brane can be regarded as a component of an infinite-dimensional supermultiplet of N=2, D=4 supersymmetry spontaneously broken down to N=1. The latter is described by N=1 Hermitian bosonic matrix superfield V_{mn} = V^\dagger_{nm}, [V_{mn}] = m+n, m,n=0,1,... in which the component V_{01} is identified with a chiral Goldstone N=1 multiplet associated with central charge of the N=2, D=4 superalgebra, and V_{11} obeys a specific nonlinear recursive equation providing the possibility to express V_{11} (as well as the other components V_{mn}) covariantly in terms of V_{01}. We demonstrate that the solution of V_{11} gives the right \emph{PBGS} action for the super-3-brane.