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

Abstract

We construct a class of Lie 3-algebras with an arbitrary number of pairs of generators with Lorentzian signature metric. Some examples are given and corresponding BLG models are studied. We show that such a system in general describes a supersymmetric massive vector multiplets after the ghost fields are Higgsed. Simple systems with nontrivial interaction are realized by infinite dimensional Lie 3-algebras associated with the loop algebras. The massive fields are then naturally identified with the Kaluza-Klein modes by the toroidal compactification triggered by the ghost fields. For example, Dp-brane with an (infinite dimensional) affine Lie algebra symmetry $\hat{g}$ can be identified with D(p+1)-brane with gauge symmetry $g$.

39 pages; v2: minor corrections, reference added

References in corpus (47)

• Gauge Symmetry and Supersymmetry of Multiple M2-Branes
• Algebraic structures on parallel M2-branes
• Modeling Multiple M2's
• Comments on Multiple M2-branes
• On Foundation of the Generalized Nambu Mechanics
• D-brane field theory on compact spaces
• M2 to D2
• Constraining Maximally Supersymmetric Membrane Actions
• M2 to D2 revisited
• On the algebras of BPS states
• M2-branes, 3-Lie Algebras and Plucker relations
• A Massive Study of M2-brane Proposals
• Supersymmetric Yang-Mills Theory From Lorentzian Three-Algebras
• On the Lie-algebraic origin of metric 3-algebras
• Multiple M2-branes and Generalized 3-Lie algebras
• Bagger-Lambert Theory for General Lie Algebras
• Noncommutative Gauge Theories in Matrix Theory
• Ghost-Free Superconformal Action for Multiple M2-Branes
• D2 to D2
• Dualities of the Matrix Model from T-Duality of the Type II String
• N=8 superconformal gauge theories and M2 branes
• Twisted Bundle On Quantum Torus and BPS States in Matrix Theory
• Towards a Noncommutative Geometric Approach to Matrix Compactification
• Taking off the square root of Nambu-Goto action and obtaining Filippov-Lie algebra gauge theory action
• Scaling limit of N=6 superconformal Chern-Simons theories and Lorentzian Bagger-Lambert theories
• Coulomb Branch of the Lorentzian Three Algebra Theory
• Kac-Moody Extensions of 3-Algebras and M2-branes
• On 3d N=8 Lorentzian BLG theory as a scaling limit of 3d superconformal N=6 ABJM theory
• Light-cone M5 and multiple M2-branes
• Metric Lie 3-algebras in Bagger-Lambert theory
• Topological branes, p-algebras and generalized Nahm equations
• Truncated Nambu-Poisson Bracket and Entropy Formula for Multiple Membranes
• M-Theory Superalgebra From Multiple Membranes
• SDiff Gauge Theory and the M2 Condensate
• A Survey on Nambu-Poisson Brackets
• Not One Bit of de Sitter Information
• On $E_{10}$ and the DDF construction
• D2 or M2? A Note on Membrane Scattering
• On relating multiple M2 and D2-branes
• On Superspace Actions for Multiple M2-Branes, Metric 3-Algebras and their Classification
• Cubic Matrix, Generalized Spin Algebra and Uncertainty Relation
• Relaxed Three-Algebras: Their Matrix Representations and Implications for Multi M2-brane Theory
• M2-branes Coupled to Antisymmetric Fluxes
• Higher-derivative 3-algebras
• Nambu-Lie 3-Algebras on Fuzzy 3-Manifolds
• Three lectures on 3-algebras
• Matrix Compactification On Orientifolds

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• Multiple Membranes in M-theory
• E${}_{6(6)}$ Exceptional Drinfel'd Algebras
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• Dp-branes, NS5-branes and U-duality from nonabelian (2,0) theory with Lie 3-algebra
• A No-Go Theorem for M5-brane Theory
• Nambu Bracket for M Theory
• Supersymmetry and DLCQ Limit of Lie 3-algebra Model of M-theory
• Aspects of U-duality in BLG models with Lorentzian metric 3-algebras
• Three-Algebra BFSS Matrix Theory
• Periodic Arrays of M2-Branes
• Extension of IIB Matrix Model by Three-Algebra
• Cartan-Weyl 3-algebras and the BLG Theory I: Classification of Cartan-Weyl 3-algebras
• Quantum corrections of (fuzzy) spacetimes from a supersymmetric reduced model with Filippov 3-algebra
• Four-algebraic extension of the IIB matrix model
• Multiple M-branes and 3-algebras
• A class of hermitian generalized Jordan triple systems and Chern-Simons gauge theory
• M2- and M5-branes in E11 Current Algebra Formulation of M-theory
• Metric 3-Leibniz algebras and M2-branes