Metric 3-Lie algebras for unitary Bagger-Lambert theories

Paul de Medeiros, Jose Figueroa-O'Farrill, Elena Mendez-Escobar, Patricia Ritter

Research output: Contribution to journalArticlepeer-review


We prove a structure theorem for finite-dimensional indefinite-signature metric 3-Lie algebras admitting a maximally isotropic centre. This algebraic condition indicates that all the negative-norm states in the associated Bagger-Lambert theory can be consistently decoupled from the physical Hilbert space. As an immediate application of the theorem, new examples beyond index 2 are constructed. The lagrangian for the Bagger-Lambert theory based on a general physically admissible 3-Lie algebra of this kind is obtained. Following an expansion around a suitable vacuum, the precise relationship between such theories and certain more conventional maximally supersymmetric gauge theories is found. These typically involve particular combinations of N = 8 super Yang-Mills and massive vector supermultiplets. A dictionary between the 3-Lie algebraic data and the physical parameters in the resulting gauge theories will thereby be provided.

Original languageEnglish
Article number037
Pages (from-to)-
Number of pages44
JournalJournal of High Energy Physics
Issue number4
Publication statusPublished - Apr 2009


  • AdS-CFT Correspondence
  • M-Theory


Dive into the research topics of 'Metric 3-Lie algebras for unitary Bagger-Lambert theories'. Together they form a unique fingerprint.

Cite this