On multiple M2-brane model(s) and its N=8 superspace formulation(s)

TL;DR

This paper reviews multiple M2-brane models, focusing on the BLG model with SDiff3 symmetry, and explores their superspace formulations, including superfield actions and relations to ABJM/ABJ models, highlighting new superspace approaches.

Contribution

It presents the on-shell superfield formulation of the SDiff3 BLG model in N=8 superspace and discusses superfield equations for related ABJM/ABJ models.

Findings

Superfield formulation of SDiff3 BLG model in N=8 superspace

Superfield action in pure spinor N=8 superspace

Discussion of N=6 and N=8 superfield equations for ABJM/ABJ models

Abstract

We give a brief review of Bagger-Lambert-Gustavsson (BLG) model, with emphasis on its version invariant under the volume preserving diffeomorphisms (SDiff3) symmetry. We describe the on-shell superfield formulation of this SDiff3 BLG model in standard N=8, d=3 superspace, as well as its superfield action in the pure spinor N=8 superspace. We also briefly address the Aharony-Bergman-Jafferis-Maldacena (ABJM/ABJ) model invariant under $SU(M)_{k}\times SU(N')_{-k}$ gauge symmetry, and discuss the possible form of their N=6 and, for the case of Chern-Simons level k=1,2, N=8 superfield equations.