2010/04/30 by Yu-tin Huang, Arthur E. Lipstein · 59 citations
Physics and Astronomy · #Amplitude #Black Holes and Theoretical Physics #Conjecture #Crossing #Global symmetry #Lagrangian #Nonlinear Waves and Solitons #Quantum Mechanics and Non-Hermitian Physics #Scattering amplitude #Space (punctuation) #Symmetry (geometry) #Tensor (intrinsic definition) #Yangian #hep-th
paper · pdf · doi:10.1007/jhep10(2010)007
published in Journal of High Energy Physics 2010(10) (Springer Nature) · 38 pages, 7 figures; v3: minor changes, published in JHEP
openalex publication_date 2010/10/01 · arxiv created 2010/10/11 · arxiv updated 2010/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/06
We use supertwistor space to construct scattering amplitudes of maximal superconformal theories in three and six dimensions. In both cases, the constraints of super-conformal 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.