Generalized conformal symmetry and recovery of SO(8) in multiple M2 and D2 branes

We investigate conformal symmetries of the Aharony-Bergman-Jafferis-Maldacena (ABJM) theory for multiple M2 branes and the Lorentzian Bagger-Lambert-Gustavsson (L-BLG) theory which can be obtained by taking a scaling limit k(≫N)→∞ of the ABJM theory. The conformal symmetry is maintained in the L-BLG by considering general space-time varying solutions to the constraint equations. The dual geometry is reduced to d=10 AdS4×CP3 in the scaling limit and has the same conformal symmetry. The curvature radius R satisfies lp(11)≪lp(10)≪R≪ls (lp(d) and ls are the d-dimensional Planck lengths and the string scale), and the theory is in a region where an α′ expansion is not valid. We also study how the SO(8) covariance is recovered in the AdS4×CP3 geometry by taking the scaling limit.