Multiple Membranes in M-theory

Abstract

We review developments in the theory of multiple, parallel membranes in M-theory. After discussing the inherent difficulties pertaining to a maximally supersymmetric lagrangian formulation with the appropriate field content and symmetries, we discuss how introducing the concept of 3-algebras allows for such a description. Different choices of 3-algebras lead to distinct classes of 2+1 dimensional theories with varying degrees of supersymmetry. We then describe how these are equivalent to a type of conventional superconformal Chern-Simons gauge theories at level k, coupled to bifundamental matter. Analysing the physical properties of these theories leads to the identification of a certain subclass of models with configurations of M2-branes in Z_k orbifolds of M-theory. In addition these models give rise to a whole new sector of the gauge/gravity duality in the form of an AdS_4/CFT_3 correspondence. We also discuss mass deformations, higher derivative corrections as well as the possibility of extracting information about M5-brane physics.

180 pages, 3 figures, Latex; v2: various typos corrected, clarifications, references and acknowledgements added, title modified, submitted to Physics Reports

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• M5-Branes, D4-Branes and Quantum 5D super-Yang-Mills
• On D=5 super Yang-Mills theory and (2,0) theory
• M2 to D2
• Membranes on an Orbifold
• Superconformal Indices for $\mathcal{N}=6$ Chern Simons Theories
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• M2-branes, 3-Lie Algebras and Plucker relations
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• A Massive Study of M2-brane Proposals
• (1,0) superconformal models in six dimensions
• On M5-branes in N=6 Membrane Action
• N = 8 Superconformal Chern--Simons Theories
• AdS_4/CFT_3 -- Squashed, Stretched and Warped
• Anomalous radius shift in AdS(4)/CFT(3)
• On the Lie-algebraic origin of metric 3-algebras
• Bagger-Lambert Theory for General Lie Algebras
• Notes on Supersymmetry Enhancement of ABJM Theory
• A Non-Abelian Self-Dual Gauge Theory in 5+1 Dimensions
• M-theory branes and their interactions
• The fuzzy S^2 structure of M2-M5 systems in ABJM membrane theories
• Massive type IIA string theory cannot be strongly coupled
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• BLG-motivated Lagrangian formulation for the chiral two-form gauge field in D=6 and M5-branes
• M2-M5 Systems in N=6 Chern-Simons Theory
• M2-Branes and Background Fields
• The Power of the Higgs Mechanism: Higher-Derivative BLG Theories
• A note on the M2-M5 brane system and fuzzy spheres
• Light-cone M5 and multiple M2-branes
• The Superconformal Gaugings in Three Dimensions
• Lorentzian Lie (3-)algebra and toroidal compactification of M/string theory
• Multiple D2-Brane Action from M2-Branes
• N=6 Superspace Constraints, SUSY Enhancement and Monopole Operators
• Scattering in ABJ theories
• Metric 3-Lie algebras for unitary Bagger-Lambert theories
• Non-planar ABJ Theory and Parity
• Three-Algebras in N = 5, 6 Superconformal Chern-Simons Theories: Representations and Relations
• Relaxed Three-Algebras: Their Matrix Representations and Implications for Multi M2-brane Theory
• The 3-Lie Algebra (2,0) Tensor Multiplet and Equations of Motion on Loop Space
• 5D Yang-Mills instantons from ABJM Monopoles
• Constructing Self-Dual Strings
• An associative star-three-product and applications to M two/M five-brane theory
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• A New Three-Algebra Representation for the {\cal N}=6 su(N)Xsu(N) Superconformal Chern-Simons Theory
• N=5 three-algebras and 5-graded Lie superalgebras
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• Unquenched massive flavors and flows in Chern-Simons matter theories
• Wilson loops at large $N$ and the quantum M2 brane
• Poincaré Series, 3d Gravity and Averages of Rational CFT
• Construction of 6D supersymmetric field models in N=(1,0) harmonic superspace
• Tri-vector deformations in $d=11$ supergravity
• Semistrict Higher Gauge Theory
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• Twisted Cohomotopy implies level quantization of the full 6d Wess-Zumino term of the M5-brane
• Localization at large N in Chern-Simons-matter theories
• Surface operators in the 6d $\mathcal{N}=(2,0)$ theory
• $G_2$-structures and quantization of non-geometric M-theory backgrounds
• Gauge enhancement of super M-branes via parametrized stable homotopy theory
• Reflection groups and 3d $\mathcal{N}\ge$ 6 SCFTs
• Duality-symmetric actions for non-Abelian tensor fields
• Real ADE-equivariant (co)homotopy and Super M-branes
• M/F-Theory as Mf-Theory
• Yang-Mills as massive Chern-Simons theory: a third way to three-dimensional gauge theories
• Comments on ABJM free energy on $S^3$ at large $N$ and perturbative expansions in M-theory and string theory
• Fermi surface behavior in the ABJM M2-brane theory
• Crisis on Infinite Earths: Short-lived de Sitter Vacua in the String Theory Landscape
• Double-Trace Flows and the Swampland
• Lessons from M2's and Hopes for M5's
• Higher T-duality in M-theory via local supersymmetry
• Leading low-energy effective action in the 6D hypermultiplet theory on a vector/tensor background
• The Third Way to Interacting $p$-form Theories
• Carroll membranes
• Effective actions in $\mathcal{N}$=1, D5 supersymmetric gauge theories: harmonic superspace approach
• A New String in Ten Dimensions?
• M2-Branes And The (2,0) Superalgebra
• Flows between Dualities for 3d Chern-Simons Theories
• On the component structure of one-loop effective actions in $6D$, $\mathcal{N}=(1,0)$ and $\mathcal{N}=(1,1)$ supersymmetric gauge theories
• Stringy Membranes in AdS/CFT
• Knot Invariants and M-Theory I: Hitchin Equations, Chern-Simons Actions, and the Surface Operators
• On gauge dependence of the one-loop divergences in $6D$, $\mathcal{N}=(1,0)$ and $\mathcal{N}=(1,1)$ SYM theories
• Fermionic Response in Finite-Density ABJM Theory with Broken Symmetry
• Dual Localized Objects From M-Branes Over AdS_4 x S^7/Z_k
• Quantum phase transitions with dynamical flavors
• A Holographic Bound for D3-Brane
• The Third way to 3D Supersymmetric Massive Yang-Mills Theory
• Supersymmetric action for multiple D0-brane system
• Higher spins from Nambu-Chern-Simons theory
• Spontaneous breaking of nilpotent symmetry in boundary BLG theory
• Low-energy $6D$, $\mathcal{N}=(1,1)$ SYM effective action beyond the leading approximation
• 3D supersymmetric nonlinear multiple D$0$-brane action and 4D counterpart of multiple M-wave system
• Supersymmetric non-Abelian multiwaves in D=3 AdS superspace
• A Nonabelian $(1,0)$ Tensor Multiplet Theory in 6D
• Matrix Quantization of Classical Nambu Brackets and Super $p$-Branes
• Supermembrane limit of Yang-Mills theory
• A path to confine gluons and fermions through complex gauge theory
• Quantum calculation of the low-energy effective action in $5D$, $\mathcal{N}=2$ SYM theory
• Heterotic M2-branes
• k-Leibniz algebras from lower order ones: from Lie triple to Lie l-ple systems
• M5-brane prongs, string soliton bound states and wall-crossing
• A 6D nonabelian $(1,0)$ Theory
• Supersymmetry at BLTP: Recent Progress in Two Directions