Comments on Higher Order BLG Supersymmetry Transformations

TL;DR

This paper investigates higher-order $l_p^3$ corrections to supersymmetry transformations in BLG theory using dNS duality, providing new insights into the structure of these corrections for abelian and non-abelian cases.

Contribution

It uniquely determines the $l_p^3$ supersymmetry corrections for scalar and fermion fields in abelian BLG and extends this to fermion corrections in non-abelian BLG using duality transformations.

Findings

Successfully derived $l_p^3$ corrections for abelian BLG supersymmetry transformations.

Extended the derivation to include fermion corrections in non-abelian BLG.

Provided observations on applying dNS duality at the supersymmetry level.

Abstract

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.