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Scattering in ABJ theories

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Abstract

We study the correspondence between scattering amplitudes and Wilson loops in three-dimensional Chern-Simons matter theories. In particular, using \( \mathcal{N} = {2} \) superspace formalism, we compute at one loop the whole spectrum of four-point superamplitudes for generic \( \mathcal{N} \geqslant {2} \) supersymmetric theories and find a vanishing result for \( \mathcal{N} = {6} \) ABJ(M) and \( \mathcal{N} = {8} \) BLG models. This restricts the possible range of theories for which Wilson loops/scattering amplitudes duality might work. At two loops, we present the computation of the four-point ABJ scattering amplitude for external chiral superfields. Extending the known result for the ABJM Wilson loop to the ABJ case we find perfect agreement. We also discuss the dual conformal invariance of our results and the relationship between the Feynman diagram computation and unitarity methods. While for the ABJM theory dual conformally invariant integrals exactly reproduce the amplitude, for the ABJ case this happens only up to a residual constant depending on the parity-violating parameter. Finally we propose a BDS-like exponentiation for the amplitude based on an analogy with the four dimensional \( \mathcal{N} = {4} \) SYM case, and discuss its strong coupling dual counterpart.

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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 G. Celoria 16, I-20133, Milano, Italy

    Andrea Mauri

  3. INFN, Sezione di Milano, Via G. 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: 1110.0738

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Bianchi, M.S., Leoni, M., Mauri, A. et al. Scattering in ABJ theories. J. High Energ. Phys. 2011, 73 (2011). https://doi.org/10.1007/JHEP12(2011)073

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