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Scattering amplitudes/Wilson loop duality in ABJM theory

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Abstract

For \( \mathcal{N} = 6 \) superconformal Chern-Simons-matter theories in three dimensions, by a direct superspace Feynman diagram approach, we compute the two-loop four-point scattering amplitude with external chiral matter fields. We find that the result is in perfect agreement with the two-loop result for a light-like four-polygon Wilson loop. This is the first non-trivial evidence that an amplitudes/Wilson loop duality might work in three dimensions. Moreover, both the IR divergent and the finite parts of our two-loop result agree with a BDS-like ansatz for all-loop amplitudes where the scaling function is given in terms of the \( \mathcal{N} = 4 \) SYM one, according to the conjectured Bethe equations for ABJM. Consequently, we are able to make a prediction for the four-loop correction to the amplitude. We also discuss the dual conformal invariance of the two-loop result.

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Authors and Affiliations

  1. Dipartimento di Fisica, Università di Milano-Bicocca and INFN, Sezione di Milano-Bicocca, Piazza della Scienza 3, I-20126, Milano, Italy

    Marco S. Bianchi, Matias Leoni & Silvia Penati

  2. Dipartimento di Fisica, Università degli Studi di Milano, Via Celoria 16, I-20133, Milano, Italy

    Andrea Mauri

  3. INFN, Sezione di Milano, Via Celoria 16, I-20133, Milano, Italy

    Andrea Mauri & Alberto Santambrogio

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  1. Marco S. Bianchi
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  2. Matias Leoni
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  3. Andrea Mauri
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  4. Silvia Penati
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  5. Alberto Santambrogio
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Correspondence to Marco S. Bianchi.

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Arxiv Eprint: 1107.3139

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Bianchi, M.S., Leoni, M., Mauri, A. et al. Scattering amplitudes/Wilson loop duality in ABJM theory. J. High Energ. Phys. 2012, 56 (2012). https://doi.org/10.1007/JHEP01(2012)056

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