Amplitudes of 3D and 6D Maximal Superconformal Theories in Supertwistor Space
arXiv:1004.4735 · doi:10.1007/JHEP10(2010)007
Abstract
We use supertwistor space to construct scattering amplitudes of maximal superconformal theories in three and six dimensions. In both cases, the constraints of superconformal invariance and rationality imply that the three-point amplitude vanishes on-shell, which constrains the four-point amplitude to have vanishing residues in all channels. In three dimensions, we find a unique solution for the four-point amplitude and demonstrate that it agrees with the component result in the BLG theory. This suggests that BLG is the unique three-dimensional theory with classical OSp(8|4) symmetry that admits a Lagrangian description. We also show that one can derive the four-point amplitude of the ABJM theory from our N=8 result by reducing the supersymmetry, which implies that the tree-level Yangian symmetry recently found in ABJM is also present in BLG. In six dimensions, we find that the consistency conditions imply that all tree-level amplitudes vanish. This leads us to conjecture that an interacting six-dimensional theory with classical OSp(8|4) symmetry does not have a Lagrangian description, local or nonlocal, unless the (2,0) tensor multiplets are supplemented by additional degrees of freedom.
arXiv comment38 pages, 7 figures; v3: minor changes, published in JHEP
References in corpus (45)
- N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals
- Direct Proof Of Tree-Level Recursion Relation In Yang-Mills Theory
- One-Loop n-Point Gauge Theory Amplitudes, Unitarity and Collinear Limits
- Perturbative Gauge Theory As A String Theory In Twistor Space
- Fusing Gauge Theory Tree Amplitudes Into Loop Amplitudes
- New Recursion Relations for Tree Amplitudes of Gluons
- Algebraic structures on parallel M2-branes
- Gluon scattering amplitudes at strong coupling
- MHV Vertices And Tree Amplitudes In Gauge Theory
- Comments on Multiple M2-branes
- Dual superconformal symmetry of scattering amplitudes in N=4 super-Yang-Mills theory
- Open P-Branes
- Phase Transitions In M-Theory And F-Theory
- Comments on String Dynamics in Six Dimensions
- One-Loop Amplitudes for e^+ e^- to Four Partons
- Superconformal Chern-Simons Theories and AdS_4/CFT_3 Correspondence
- Covariant Action for the Super-Five-Brane of M-Theory
- Small Instantons and Tensionless Non-critical Strings
- Yangian symmetry of scattering amplitudes in N=4 super Yang-Mills theory
- A Duality For The S Matrix
- Fermionic T-Duality, Dual Superconformal Symmetry, and the Amplitude/Wilson Loop Connection
- World-Volume Action of the M Theory Five-Brane
- Comments on the Bagger-Lambert theory and multiple M2-branes
- Non-trivial Fixed Points of The Renormalization Group in Six Dimensions
- Interacting Chiral Gauge Fields in Six Dimensions and Born-Infeld Theory
- Constraining Maximally Supersymmetric Membrane Actions
- Amplitudes and Spinor-Helicity in Six Dimensions
- M 5-brane and superconformal (0,2) tensor multiplet in 6 dimensions
- BPS Spectrum of the Five-Brane and Black Hole Entropy
- Studies of the ABJM Theory in a Formulation with Manifest SU(4) R-Symmetry
- Exacting N=4 Superconformal Symmetry
- N = 8 Superconformal Chern--Simons Theories
- Supertwistor space for 6D maximal super Yang-Mills
- Six-Dimensional Tensionless Strings In The Large N Limit
- One-loop corrections to Bagger-Lambert theory
- Scattering in Mass-Deformed N>=4 Chern-Simons Models
- Symmetries and analytic properties of scattering amplitudes in N=4 SYM theory
- Recursion Relations, Generating Functions, and Unitarity Sums in N=4 SYM Theory
- Superconformal invariants for scattering amplitudes in N=4 SYM theory
- Boundaries in M-Theory
- Covariant representation theory of the Poincaré algebra and some of its extensions
- Covariant actions for N=1, D=6 Supergravity theories with chiral bosons
- N=8 Superspace Constraints for Three-dimensional Gauge Theories
- First-quantized N=4 Yang-Mills
- Conformal superfields and BPS states in AdS_4/7 geometries
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- Generic multiloop methods and application to N=4 super-Yang-Mills
- Equivalent D=3 Supergravity Amplitudes from Double Copies of Three-Algebra and Two-Algebra Gauge Theories
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- Dual Superconformal Symmetry of N=6 Chern-Simons Theory
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- Dualities for Loop Amplitudes of N=6 Chern-Simons Matter Theory
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- , and theories
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- The S Matrix of 6D Super Yang-Mills and Maximal Supergravity from Rational Maps
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- On Twistors and Conformal Field Theories from Six Dimensions
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- Soft theorems from anomalous symmetries
- On the ABJM four-point amplitude at three loops and BDS exponentiation
- Supersymmetry and Mass Gap in 2+1 Dimensions: A Gauge Invariant Hamiltonian Analysis
- Chiral Squaring
- Positroid Stratification of Orthogonal Grassmannian and ABJM Amplitudes
- 5d and 6d SCFTs Have No Weak Coupling Limit
- Consistency conditions from generalized-unitarity
- Bootstrap and Amplitudes: A Hike in the Landscape of Quantum Field Theory
- ABJM amplitudes and WL at finite N
- Minitwistors and 3d Yang-Mills-Higgs theory
- Recursion and worldsheet formulae for 6d superamplitudes
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- 6d Dual Conformal Symmetry and Minimal Volumes in AdS
- Scattering Amplitudes of Massive N=2 Gauge Theories in Three Dimensions
- Hopf-Wess-Zumino term in the effective action of the 6d, (2, 0) field theory revisted
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- Conformally Invariant Spinorial Equations in Six Dimensions
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- Symplectic Grassmannians, dual conformal symmetry and 4-point amplitudes in 6D
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