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On-shell superamplitudes in \( \mathcal{N} < 4 \) SYM

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Abstract

We present an on-shell formalism for superamplitudes of pure \( \mathcal{N} < 4 \) super Yang-Mills theory. Two superfields, Φ and Φ†, are required to describe the two CPT conjugate supermultiplets. Simple truncation prescriptions allow us to derive explicit tree-level MHV and NMHV superamplitudes with \( \mathcal{N} \)-fold SUSY. Any \( \mathcal{N} = 0,1,2 \) tree superamplitudes have large-z falloffs under super-BCFW shifts, except under [Φ, Φ†〉-shifts. We show that this ‘bad’ shift is responsible for the bubble contributions to 1-loop amplitudes in \( \mathcal{N} = 0,1,2 \) SYM. We evaluate the MHV bubble coefficients in a manifestly supersymmetric form and demonstrate for the case of four external particles that the sum of bubble coefficients is equal to minus the tree superamplitude times the 1-loop beta-function coefficient. The connection to the beta-function is expected since only bubble integrals capture UV divergences; we discuss briefly how the minus sign arises from UV and IR divergences in dimensional regularization.

Other applications of the on-shell formalism include a solution to the NK MHV \( \mathcal{N} = 1 \) SUSY Ward identities and a clear description of the connection between 6d superamplitudes and the 4d ones for both \( \mathcal{N} = 4 \) and \( \mathcal{N} = 2 \) SYM. We outline extensions to \( \mathcal{N} < 8 \) super-gravity.

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Authors and Affiliations

  1. Michigan Center for Theoretical Physics, Department of Physics, University of Michigan, 450 Church Street, Ann Arbor, MI, 48109-1040, U.S.A.

    Henriette Elvang & Cheng Peng

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

    Yu-tin Huang

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  1. Henriette Elvang
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  2. Yu-tin Huang
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Correspondence to Cheng Peng.

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Elvang, H., Huang, Yt. & Peng, C. On-shell superamplitudes in \( \mathcal{N} < 4 \) SYM. J. High Energ. Phys. 2011, 31 (2011). https://doi.org/10.1007/JHEP09(2011)031

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