Supersymmetric Yang-Mills Theory From Lorentzian Three-Algebras

TL;DR

This paper extends the Bagger-Lambert theory with a ghost sector to establish a BRST symmetry, demonstrating the absence of negative norm states and connecting to maximally supersymmetric Yang-Mills theory.

Contribution

It introduces a BRST-invariant extension of Lorentzian three-algebra based Bagger-Lambert theory, linking it to 2+1D maximally supersymmetric Yang-Mills theory.

Findings

BRST symmetry removes negative norm states.

Theory with scalar vev is equivalent to superconformal Yang-Mills.

Trivial vacuum expansion yields a trivial theory.

Abstract

We show that by adding a supersymmetric Faddeev-Popov ghost sector to the recently constructed Bagger-Lambert theory based on a Lorentzian three algebra, we obtain an action with a BRST symmetry that can be used to demonstrate the absence of negative norm states in the physical Hilbert space. We show that the combined theory, expanded about its trivial vacuum, is BRST equivalent to a trivial theory, while the theory with a vev for one of the scalars associated with a null direction in the three-algebra is equivalent to a reformulation of maximally supersymmetric 2+1 dimensional Yang-Mills theory in which there a formal SO(8) superconformal invariance.