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Tree-level recursion relation and dual superconformal symmetry of the ABJM theory

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Abstract

We propose a recursion relation for tree-level scattering amplitudes in three-dimensional Chern-Simons-matter theories. The recursion relation involves a complex deformation of momenta which generalizes the BCFW-deformation used in higher dimensions. Using background field methods, we show that all tree-level superamplitudes of the ABJM theory vanish for large deformations, establishing the validity of the recursion formula. Furthermore, we use the recursion relation to compute six-point and eight-point component amplitudes and match them with independent computations based on Feynman diagrams or the Grassmannian integral formula. As an application of the recursion relation, we prove that all tree-level amplitudes of the ABJM theory have dual superconformal symmetry. Using generalized unitarity methods, we extend this symmetry to the cut-constructible parts of the loop amplitudes.

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Authors and Affiliations

  1. School of Physics, Korea Institute for Advanced Study, Seoul, 130–722, Korea

    Dongmin Gang & Eunkyung Koh

  2. Department of Physics and Astronomy, UCLA, Los Angeles, CA, 90095–1547, U.S.A.

    Yu-tin Huang

  3. Department of Physics, University of Seoul, Seoul, 130–743, Korea

    Sangmin Lee

  4. Department of Physics, California Institute of Technology, Pasadena, CA, 91125, U.S.A.

    Arthur E. Lipstein

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  1. Dongmin Gang
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  2. Yu-tin Huang
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Correspondence to Sangmin Lee.

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ArXiv ePrint: 1012.5032

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Gang, D., Huang, Yt., Koh, E. et al. Tree-level recursion relation and dual superconformal symmetry of the ABJM theory. J. High Energ. Phys. 2011, 116 (2011). https://doi.org/10.1007/JHEP03(2011)116

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