Comments on Higher Order BLG Supersymmetry Transformations

In this paper we begin an investigation into the \(l_p^3\) corrections to the supersymmetry transformations of the Bagger-Lambert-Gustavsson (BLG) theory. We begin with a review of the dNS duality transformation which allows a non-abelian gauge field to be dualised to a scalar field in 2+1 dimensions. Applying this duality to \(\alpha'^2\) terms of the non-abelian D2-brane theory gives rise to the \(l_p^3\) corrections of the Lorentzian BLG theory. We then apply this duality transformation to the \(\alpha'^2\) corrections of the D2-brane supersymmetry transformations. For the `abelian' BLG theory we are able to uniquely determine the \(l_p^3\) corrections to the supersymmetry transformations of the scalar and fermion fields. Generalising to the `non-abelian' BLG theory we are able to determine the \(l_p^3\) correction to the supersymmetry transformation of the fermion field. Along the way make a number of observations relating to the implementation of the dNS duality transformation at the level of supersymmetry transformations.