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An all order identity between ABJM and \( \mathcal{N} \) = 4 SYM four-point amplitudes

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Abstract

We derive an exact algebraic identity between the two-loop four-point amplitude in ABJM theory and the corresponding one-loop amplitude in \( \mathcal{N} \) = 4 SYM theory. This identity generalizes previous partial results to an exact relation valid at all orders in the IR regulator. Moreover, it allows to conjecture an exact iterative expression for the complete three dimensional amplitude in terms of the BDS ansatz for the four dimensional one, indicating that the strict relation between the two amplitudes experimented at two loops might propagate to all orders. In particular, an almost complete expression for the ABJM amplitude at four loops is derived.

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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

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  1. Marco S. Bianchi
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  2. Matias Leoni
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  3. Silvia Penati
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Correspondence to Marco S. Bianchi.

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ArXiv ePrint: 1112.3649

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Bianchi, M.S., Leoni, M. & Penati, S. An all order identity between ABJM and \( \mathcal{N} \) = 4 SYM four-point amplitudes. J. High Energ. Phys. 2012, 45 (2012). https://doi.org/10.1007/JHEP04(2012)045

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