2008/05/31 by Jaume Gomis, Giuseppe Milanesi, Jorge G. Russo +1 · 2 citations
Mathematics · Physics and Astronomy · #Antisymmetric tensor #BRST quantization #Black Holes and Theoretical Physics #Gauge symmetry #Gauge theory #Homotopy and Cohomology in Algebraic Topology #Lie algebra #Noncommutative and Quantum Gravity Theories #Quantum field theory #Structure constants #Supersymmetric gauge theory #Unitarity #hep-th
paper · pdf · doi:10.1088/1126-6708/2008/06/075
published as JHEP 0806:075,2008 · 12 pages, Latex; small corrections and references added; published version (small typos fixed)
arxiv created 2008/06/15 · openalex publication_date 2008/06/24 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We construct the totally antisymmetric structure constants fABCD of a 3-algebra with a Lorentzian bi-invariant metric starting from an arbitrary semi-simple Lie algebra. The structure constants fABCD can be used to write down a maximally superconformal 3d theory that incorporates the expected degrees of freedom of multiple M2 branes, including the "center-of-mass" mode described by free scalar and fermion fields. The gauge field sector reduces to a three dimensional BF term, which underlies the gauge symmetry of the theory. We comment on the issue of unitarity of the quantum theory, which is problematic, despite the fact that the specific form of the interactions prevent the ghost fields from running in the internal lines of any Feynman diagram. Giving an expectation value to one of the scalar fields leads to the maximally supersymmetric 3d Yang-Mills Lagrangian with the addition of two U(1) multiplets, one of them ghost-like, which is decoupled at large gYM.