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Amplitudes of 3D and 6D maximal superconformal theories in supertwistor space

Huang, Yu-tin and Lipstein, Arthur E. (2010) Amplitudes of 3D and 6D maximal superconformal theories in supertwistor space. Journal of High Energy Physics, 2010 (10). Art. No. 007. ISSN 1126-6708. doi:10.1007/JHEP10(2010)007.

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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 nd 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.

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Lipstein, Arthur E.0000-0002-0213-186X
Additional Information:© 2010 Springer. This article is distributed under the terms of the Creative Commons Attribution Noncommercial License which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited. Received: July 15, 2010; revised: September 3, 2010; accepted: September 4, 2010; published: October 4, 2010. The work of YH is supported by the US DOE grant DE-FG03-91ER40662 and the work of AEL is supported in part by the US DOE grant DE-FG02-92ER40701. We thank Zvi Bern, Tristan Deenen, Eric D'Hoker and John H. Schwarz for many detailed and enlightening discussions. We would also like to thank Till Bargheer, Pei Ming Ho, Harold Ita, F. Loebbert, Carlo Meneghelli, Donal O'Connell, Warren Siegel, George Sterman, and Ilmo Sung for useful comments. YH would like to thank Mark Wise for the invitation as visiting scholar at Caltech.
Group:Caltech Theory
Funding AgencyGrant Number
Department of Energy (DOE)DE-FG03-91ER40662
Department of Energy (DOE)DE-FG02-92ER40701
Subject Keywords:Supersymmetric gauge theory; Superspaces; Conformal Field Models in String Theory
Issue or Number:10
Record Number:CaltechAUTHORS:20110112-150921234
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:21740
Deposited On:14 Jan 2011 17:30
Last Modified:09 Nov 2021 16:00

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