Generalized Conformal Symmetry and Recovery of SO(8) in Multiple M2 and D2 Branes

TL;DR

This paper explores the conformal symmetries of ABJM and L-BLG theories for multiple M2 branes, showing how SO(8) symmetry is recovered in the dual geometry through a specific scaling limit.

Contribution

It demonstrates the preservation of conformal symmetry in L-BLG via space-time varying solutions and elucidates the geometric recovery of SO(8) symmetry in the dual AdS4 x CP3 background.

Findings

Conformal symmetry is maintained in L-BLG with general solutions.

Dual geometry reduces to d=10 AdS4 x CP3 in the scaling limit.

SO(8) covariance is recovered in the dual geometry.

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) -> \infty 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 x CP3 in the scaling limit and has the same conformal symmetry. The curvature radius R satisfies l_{11p} << l_{10p} << R << l_s (l_{dp} and l_s are the d-dimensional Planck lengths and the string scale), and the theory is in a region where an \alpha' expansion is not valid. We also study how the SO(8) covariance is recovered in the AdS4 x CP3 geometry by taking the scaling limit.