Comments on Higher Order BLG Supersymmetry Transformations

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 ${\alpha }^{\prime 2}$ 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 ${\alpha }^{\prime 2}$ 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.

34 pages; References added

References in corpus (9)

• Gauge Symmetry and Supersymmetry of Multiple M2-Branes
• Algebraic structures on parallel M2-branes
• Modeling Multiple M2's
• Janus field theories from multiple M2 branes
• Scaling limit of N=6 superconformal Chern-Simons theories and Lorentzian Bagger-Lambert theories
• On 3d N=8 Lorentzian BLG theory as a scaling limit of 3d superconformal N=6 ABJM theory
• Multiple D2-Brane Action from M2-Branes
• D2 to M2 Procedure for D2-Brane DBI Effective Action
• On non-linear action of multiple M2-branes

Cited by in corpus (1)

• Aspects of Supersymmetry in Multiple Membrane Theories