Metric 3-Lie algebras for unitary Bagger-Lambert theories

Feb, 2009
38 pages
Published in:
  • JHEP 04 (2009) 037
e-Print:
Report number:
  • EMPG-09-02

Citations per year

200920132017202120230246810
Abstract: (arXiv)
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.
Note:
  • 38 pages
  • algebra: Lie
  • gauge field theory: Yang-Mills
  • Hilbert space
  • supersymmetry
  • Bagger-Lambert-Gustavsson model
  • space-time: signature