Ghost-Free Superconformal Action for Multiple M2-Branes

Abstract

The Bagger--Lambert construction of N = 8 superconformal field theories (SCFT) in three dimensions is based on 3-algebras. Three groups of researchers recently realized that an arbitrary semisimple Lie algebra can be incorporated by using a suitable Lorentzian signature 3-algebra. The SU(N) case is a candidate for the SCFT describing coincident M2-branes. However, these theories contain ghost degrees of freedom, which is unsatisfactory. We modify them by gauging certain global symmetries. This eliminates the ghosts from these theories while preserving all of their desirable properties. The resulting theories turn out to be precisely equivalent to N = 8 super Yang--Mills theories.

11 pages; v2: minor clarifications and mention of subsequent work

Cited by in corpus (54)

• Three-Algebras and N=6 Chern-Simons Gauge Theories
• On Type IIA Penrose Limit and N=6 Chern-Simons Theories
• n-ary algebras: a review with applications
• Tilings, Chern-Simons Theories and M2 Branes
• (1,0) superconformal models in six dimensions
• The complete AdS(4) x CP(3) superspace for the type IIA superstring and D-branes
• Multiple M2-branes and Generalized 3-Lie algebras
• Multiple Membranes in M-theory
• Membranes with a boundary
• ABJM models in N=3 harmonic superspace
• Boundary Conditions for Interacting Membranes
• The fuzzy S^2 structure of M2-M5 systems in ABJM membrane theories
• Towards the Quantum Geometry of the M5-brane in a Constant C-Field from Multiple Membranes
• Multiple Membranes from Gauged Supergravity
• From N M2's to N D2's
• Scaling limit of N=6 superconformal Chern-Simons theories and Lorentzian Bagger-Lambert theories
• On 3d N=8 Lorentzian BLG theory as a scaling limit of 3d superconformal N=6 ABJM theory
• The Power of the Higgs Mechanism: Higher-Derivative BLG Theories
• Light-cone M5 and multiple M2-branes
• Lorentzian Lie (3-)algebra and toroidal compactification of M/string theory
• Non-linear theory for multiple M2 branes
• Multiple M2-Branes and Plane Waves
• Metric 3-Lie algebras for unitary Bagger-Lambert theories
• The AdS(4) x CP(3) string and its Bethe equations in the near plane wave limit
• Relaxed Three-Algebras: Their Matrix Representations and Implications for Multi M2-brane Theory
• Symplectic Three-Algebra Unifying N=5,6 Superconformal Chern-Simons-Matter Theories
• Generalized Conformal Symmetry and Recovery of SO(8) in Multiple M2 and D2 Branes
• Super-Yang-Mills and M5-branes
• N=6 Membrane Worldvolume Superalgebra
• M-Theory and Maximally Supersymmetric Gauge Theories
• Model of M-theory with Eleven Matrices
• On the worldsheet theory of the type IIA AdS(4) x CP(3) superstring
• Supersymmetry and DLCQ Limit of Lie 3-algebra Model of M-theory
• A New Three-Algebra Representation for the {\cal N}=6 su(N)Xsu(N) Superconformal Chern-Simons Theory
• Aspects of U-duality in BLG models with Lorentzian metric 3-algebras
• Abelian Vortex in Bagger-Lambert-Gustavsson Theory
• Squashing Gravity Dual of N=6 Superconformal Chern-Simons Gauge Theory
• Triality and Bagger-Lambert Theory
• Light-cone analysis of ungauged and topologically gauged BLG theories
• Three-Algebra BFSS Matrix Theory
• On thermodynamics of N=6 superconformal Chern-Simons theory
• Remark About Scaling Limit of ABJ Theory
• On Dielectric Membranes
• Nambu-Poisson Bracket and M-Theory Branes Coupled to Antisymmetric Fluxes
• The Yang-Mills and chiral fields in six dimensions
• Cartan-Weyl 3-algebras and the BLG Theory I: Classification of Cartan-Weyl 3-algebras
• A N=8 action for multiple M2-branes with an arbitrary number of colors
• More on the scalar-tensor B-F theory
• Open M2-branes with Flux and Modified Basu-Harvey Equation
• Branes from a non-Abelian (2,0) tensor multiplet with 3-algebra
• A class of hermitian generalized Jordan triple systems and Chern-Simons gauge theory
• Janus Field Theories from Non-Linear BF Theories for Multiple M2-Branes
• F-string Solution in AdS4 X CP3 PP-wave Background
• Mass Deformed L-BLG Theory From ABJ Theory