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

TL;DR

This paper demonstrates how the N=8 superconformal Bagger-Lambert theory can be derived from the N=6 superconformal Chern-Simons-matter theories through a specific scaling limit, revealing a connection between different superconformal models.

Contribution

It introduces a scaling limit that derives the Lorentzian Bagger-Lambert theory from N=6 theories, establishing a link between these superconformal models.

Findings

Derivation of N=8 theory from N=6 theories via scaling limit.

Identification of a generalized conformal symmetry in the scaled theory.

Description of N=8 supersymmetric 2-brane theory with space-time dependent coupling.

Abstract

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. In this scaling limit, M2-branes are located far from the origin of C^4/Z_k compared to their fluctuations and Z_k identification becomes a circle identification. Hence the scaled theory describes N=8 supersymmetric theory of 2-branes with dynamical coupling. The coupling constant is promoted to a space-time dependent SO(8) vector X_0^I and we show that the scaled theory has a generalized conformal symmetry as well as manifest SO(8) with the transformation of the background fields X_0^I.