Supersymmetric Yang-Mills theory from lorentzian three-algebras

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.

Lorentzian Lie (3-)algebra and toroidal compactification of M/string theory

“…In section 2, we first review the Lorentzian BLG model [14][15][16]. We describe the typical structure of the 3-algebra for which the removal of the ghost field [18,19] is possible. In section 3, we give a detailed study of the constraint from the fundamental identity.…”

“…ghost fields can be made more rigorous [18,19] by gauging this global symmetry. Namely by adding extra gauge fields C µ , χ through…”

“…As already reviewed in section 2, we solve them by the assignment [16] or the introduction of extra gauge symmetry [18,19]:…”

Superconformal M2-branes and generalized Jordan triple systems

“…Even when this is the case they are of real interest only if they contain genuine M2-physics instead of just providing a reformulation of the D2-brane. For some recent results in this direction, see [14][15][16][17].…”

Superconformal Chern-Simons theories and the squashed seven sphere

“…The theory has SO(4) gauge symmetry. There have been numerous subsequent attempts to generalize the theory especially to extend to the gauge group other than SO(4) [6][7][8][9][10][11][12][13]. More recently, Aharony, Bergman, Jafferis and Maldacena [14] discovered a family of N = 6 superconformal Chern-Simons theories with matter fields.…”