Ghost-Free Superconformal Action for Multiple M2-Branes

TL;DR

The paper investigates ghost degrees of freedom in Lorentzian Bagger–Lambert theories for multiple M2-branes and proposes gauging global shift symmetries to remove ghosts. By introducing a dimension-$\tfrac{3}{2}$ Stückelberg field and, in the full BL theory, new fields $C_\mu^I$ and a Majorana–Weyl spinor $\chi$, the authors achieve ghost elimination while preserving ${\cal N}=8$ supersymmetry and conformal structure; on fixing the gauge, the theory reduces to maximally supersymmetric 3d Yang–Mills with coupling $g_{\rm YM}$, signaling spontaneous breaking of conformal invariance. Consequently, the Lorentzian BL construction does not yield a new conformal fixed point in flat space, and the only genuinely new MS SCFT remains the positive-definite $SO(4)$ BL theory. The work clarifies limitations of Lorentzian 3-algebras for M2-brane SCFTs and motivates exploring alternative 3-algebra frameworks.

Abstract

The Bagger--Lambert construction of N = 8 superconformal field theories (SCFT) in three dimensions is based on 3-algebras. Three groups of researchers recently realized that an arbitrary semisimple Lie algebra can be incorporated by using a suitable Lorentzian signature 3-algebra. The SU(N) case is a candidate for the SCFT describing coincident M2-branes. However, these theories contain ghost degrees of freedom, which is unsatisfactory. We modify them by gauging certain global symmetries. This eliminates the ghosts from these theories while preserving all of their desirable properties. The resulting theories turn out to be precisely equivalent to N = 8 super Yang--Mills theories.