Quiver Chern-Simons Theories, D3-branes and Lorentzian Lie 3-algebras

We show that the Bagger-Lambert-Gustavsson (BLG) theory with two pairs of negative norm generators is derived from the scaling limit of an orbifolded Aharony-Bergman-Jafferis-Maldacena (ABJM) theory. The BLG theory with many Lorentzian pairs is known to be reduced to the Dp-brane theory via Higgs mechanism, so our scaling procedure can be used to derive Dp-branes directly from M2-branes in the field theory language. In this paper, we focus on the D3-brane case and investigate the scaling limits of various quiver Chern-Simons theories obtained from different orbifolding actions. Remarkably, in the case of N=2 quiver CS theories, the resulting D3-brane action covers a larger region in the parameter space of the complex structure moduli than the N=4 quiver CS theories. We also investigate how the SL(2,Z) duality transformation is realized in the resultant D3-brane theory.