On 3d N=8 Lorentzian BLG theory as a scaling limit of 3d superconformal N=6 ABJM theory

Abstract

We elaborate on the suggestion made in arXiv:0806.3498 that the 3d \N=8 superconformal SU(N) Chern-Simons-matter theory of Lorentzian Bagger-Lambert-Gustavson type (L-BLG) can be obtained by a scaling limit (involving sending the level k to infinity and redefining the fields) from the \N=6 superconformal U(N)xU(N) Chern-Simons-matter theory of Aharony, Bergman, Jafferis and Maldacena (ABJM). We show that to implement such a limit in a consistent way one is to extend the ABJM theory by an abelian "ghost" multiplet. The corresponding limit at the 3-algebra level also requires extending the non-antisymmetric Bagger-Lambert 3-algebra underlying the ABJM theory by a negative-norm generator. We draw analogy with similar scaling limits discussed previously for bosonic Chern-Simons theory and comment on some implications of this relation between the ABJM and L-BLG theories.

16 pages; published version - reference added, minor corrections

References in corpus (15)

• N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals
• Gauge Symmetry and Supersymmetry of Multiple M2-Branes
• Algebraic structures on parallel M2-branes
• Modeling Multiple M2's
• Comments on the Bagger-Lambert theory and multiple M2-branes
• M2 to D2
• M2-branes, 3-Lie Algebras and Plucker relations
• N = 8 Superconformal Chern--Simons Theories
• On the Lie-algebraic origin of metric 3-algebras
• Multiple M2-branes and Generalized 3-Lie algebras
• Bagger-Lambert Theory for General Lie Algebras
• From N M2's to N D2's
• Scaling limit of N=6 superconformal Chern-Simons theories and Lorentzian Bagger-Lambert theories
• Coulomb Branch of the Lorentzian Three Algebra Theory
• D2 or M2? A Note on Membrane Scattering

Cited by in corpus (13)

• The fuzzy S^2 structure of M2-M5 systems in ABJM membrane theories
• Lorentzian Lie (3-)algebra and toroidal compactification of M/string theory
• Finite field-dependent BRST symmetry for ABJM theory in $\mathcal{N}=1$ superspace
• Super-Yang-Mills Theory in SIM(1) Superspace
• Supergravity at the boundary of AdS supergravity
• Anti-FFBRST Transformations for the BLG Theory in Presence of a Boundary
• Aspects of U-duality in BLG models with Lorentzian metric 3-algebras
• Membrane Dynamics in Three dimensional N=6 Supersymmetric Chern-Simons Theory
• Remark About Scaling Limit of ABJ Theory
• Comments on Higher Order BLG Supersymmetry Transformations
• More on the scalar-tensor B-F theory
• Aspects of Supersymmetry in Multiple Membrane Theories
• On-shell supersymmetry breaking in the Abelian Chern-Simons-matter model in three dimensions of spacetime