Generalized conformal symmetry and recovery of [formula omitted] in multiple M2 and D2 branes

Abstract

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 AdS 4 × CP 3 in the scaling limit and has the same conformal symmetry. The curvature radius R satisfies l p ( 11 ) ≪ l p ( 10 ) ≪ R ≪ l s ( l p ( d ) and l s 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 AdS 4 × CP 3 geometry by taking the scaling limit.