Scaling limit of N=6 superconformal Chern-Simons theories and Lorentzian Bagger-Lambert theories

Understand

We show that the N=8 superconformal Bagger-Lambert theory based on the Lorentzian 3-algebra can be derived by taking a certain scaling limit of the recently proposed N=6 superconformal U(N)xU(N) Chern-Simons-matter theories at level (k, -k).

• The scaling limit (and Inonu-Wigner contraction) is to scale the trace part of the bifundamental fields as X_0 -> \lambda^{-1} X_0 and an axial combination of the two gauge fields as B_{\mu} -> \lambda B_\mu.
• Simultaneously we scale the level as k -> \lambda^{-1} k and then take \lambda -> 0 limit.
• Interestingly the same constraint equation \partial^2 X_0=0 is derived by imposing finiteness of the action.