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 × 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.
Highlights
IntroductionΦ = Φ(y), Ξ = Ξ(y) and Ω = Ω(y) are functions on M 3, and ijk is the Levi-Cevita symbol (it is convenient to define Nambu brackets (NB) using a constant scalar density e [6], but this is not important for our present discussion here and we simplify the notation by setting e = 1)
In the fall of 2007, motivated by the search for a lowenergy description of the multiple M2-brane system, Bagger, Lambert and Gustavsson [1, 2, 3] proposed a N = 8 supersymmetric superconformal d = 3 model based on Filippov three algebra [4] instead of Lie algebra
Lie algebras are defined with the use of antisymmetric brackets [X, Y ] = −[Y, X] of two elements, X = XaTa and Y = Y aTa, called Lie bracka a ets or commutator
Summary
Φ = Φ(y), Ξ = Ξ(y) and Ω = Ω(y) are functions on M 3, and ijk is the Levi-Cevita symbol (it is convenient to define NB using a constant scalar density e [6], but this is not important for our present discussion here and we simplify the notation by setting e = 1) These brackets are invariant with respect to the volume preserving diffeomorphisms of M3, which we call SDiff transformations. For our discussion here it is sufficient to assume that M 3 has the topology of sphere S3 Another example of 3-algebra, which was present already in the first paper by Bagger and Lambert [1] is A4 realized by generators Ta, a = 1, 2, 3, 4 obeying.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
