M-Theory and Maximally Supersymmetric Gauge Theories

Abstract

In this informal review for non-specalists we discuss the construction of maximally supersymmetric gauge theories that arise on the worldvolumes branes in String Theory and M-Theory. Particular focus is made on the relatively recent construction of M2-brane worldvolume theories. In a formal sense, the existence of these quantum field theories can be viewed as predictions of M-Theory. Their construction is therefore a reinforcement of the ideas underlying String Theory and M-Theory. We also briefly discuss the six-dimensional conformal field theory that is expected to arise on M5-branes. The construction of this theory is not only an important open problem for M-Theory but also a significant challenge to our current understanding of quantum field theory more generally.

Minor corrections and an added acknowledgement. Accepted for publication in Annual Reviews

References in corpus (35)

• N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals
• Gauge Symmetry and Supersymmetry of Multiple M2-Branes
• Algebraic structures on parallel M2-branes
• Flux Compactification
• Modeling Multiple M2's
• Fractional M2-branes
• Comments on the Bagger-Lambert theory and multiple M2-branes
• M5-Branes, D4-Branes and Quantum 5D super-Yang-Mills
• On D=5 super Yang-Mills theory and (2,0) theory
• M2 to D2
• n-ary algebras: a review with applications
• Membranes on an Orbifold
• Physics of String Flux Compactifications
• M2-branes, 3-Lie Algebras and Plucker relations
• Supersymmetry enhancement by monopole operators
• (1,0) superconformal models in six dimensions
• N = 8 Superconformal Chern--Simons Theories
• AdS_4/CFT_3 -- Squashed, Stretched and Warped
• Multiple M2-branes and Generalized 3-Lie algebras
• Mass-Deformed Bagger-Lambert Theory and its BPS Objects
• Notes on Supersymmetry Enhancement of ABJM Theory
• Bagger-Lambert Theory for General Lie Algebras
• A Non-Abelian Self-Dual Gauge Theory in 5+1 Dimensions
• M-theory branes and their interactions
• Massive type IIA string theory cannot be strongly coupled
• N=8 superconformal gauge theories and M2 branes
• Non-abelian Action for Multiple Five-Branes with Self-Dual Tensors
• M2-Branes and Background Fields
• Light-cone M5 and multiple M2-branes
• Metric 3-Lie algebras for unitary Bagger-Lambert theories
• Three-Algebras in N = 5, 6 Superconformal Chern-Simons Theories: Representations and Relations
• An associative star-three-product and applications to M two/M five-brane theory
• Dimensional reduction of the ABJM model
• Unifying N=5 and N=6
• N=5 three-algebras and 5-graded Lie superalgebras

Cited by in corpus (16)

• Construction of 6D supersymmetric field models in N=(1,0) harmonic superspace
• Twisted Cohomotopy implies twisted String structure on M5-branes
• Duality-symmetric actions for non-Abelian tensor fields
• Super-exceptional embedding construction of the heterotic M5: Emergence of SU(2)-flavor sector
• Leading low-energy effective action in the 6D hypermultiplet theory on a vector/tensor background
• On the amplitudes in N=(1,1) D=6 SYM
• On the component structure of one-loop effective actions in $6D$, $\mathcal{N}=(1,0)$ and $\mathcal{N}=(1,1)$ supersymmetric gauge theories
• Amplitudes in fishnet theories in diverse dimensions and Box ladder diagrams
• Low-energy $6D$, $\mathcal{N}=(1,1)$ SYM effective action beyond the leading approximation
• Spontaneous breaking of nilpotent symmetry in boundary BLG theory
• Partition Functions for Maxwell Theory on the Five-torus and for the Fivebrane on S1XT5
• A Nonabelian $(1,0)$ Tensor Multiplet Theory in 6D
• Gauge protected entanglement between gravity and matter
• Ward and Nielsen Identities for ABJM Theory in $\mathcal{N}=1$ Superspace
• Quantum calculation of the low-energy effective action in $5D$, $\mathcal{N}=2$ SYM theory
• A 6D nonabelian $(1,0)$ Theory