N=8 superfield formulation of the Bagger-Lambert-Gustavsson model

TL;DR

This paper presents an N=8 superspace reformulation of the Bagger-Lambert-Gustavsson model, making its full supersymmetry explicit and simplifying its Lagrangian structure.

Contribution

It introduces a novel N=8 superspace approach using pure spinor wave functions, simplifying the model's structure and revealing its algebraic consistency.

Findings

Lagrangian contains only cubic interactions

Supersymmetry is fully manifest in the reformulation

The approach relies on pure spinor and 3-algebra interplay

Abstract

We reformulate the Bagger-Lambert-Gustavsson model using an N=8 superspace, thus making the full supersymmetry manifest. The formulation is based on appropriate "pure spinor wave functions" for the Chern-Simons and matter multiplets. The Lagrangian has an extremely simple structure, essentially containing a Chern-Simons-like term for the gauge field wave function and a minimally coupled matter wave function. No higher order interactions than cubic are present. The consistency of the setup relies on an interplay between the algebraic structures of the 3-algebra and of the pure spinors.