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Amplitudes from anomalous superconformal symmetry

Journal of High Energy Physics volume 2019, Article number: 179 (2019) Cite this article

A preprint version of the article is available at arXiv.

Abstract

We initiate a systematic study of the consequences of (super)conformal symmetry of massless scattering amplitudes. The classical symmetry is potentially broken at the quantum level by infrared and ultraviolet effects. We study its manifestations on the finite hard part of the scattering process. The conformal Ward identities in momentum space are second-order differential equations, difficult to analyze. We prefer to study superconformal symmetry whose generators are first-order in the momenta. Working in a massless \( \mathcal{N} \) = 1 supersymmetric Wess-Zumino model, we derive on-shell superconformal Ward identities. They contain an anomaly due to collinear regions of loop momenta. It is given by an integral with one loop less than the original graph, with an extra integral over a collinear splitting parameter. We discuss the relation to the holomorphic anomaly that was previously studied in tree-level amplitudes and at the level of unitarity cuts. We derive and solve Ward identities for various scattering processes in the model. We classify the on-shell superamplitudes according to their Grassmann degree, in close analogy with the helicity classification of gluon amplitudes. We focus on MHV-like and NMHV-like amplitudes with up to six external particles, at one and two loops. Interestingly, the superconformal generator acting on the bosonic part of the amplitudes is Witten’s twistor collinearity operator. We find that the first-order differential equations, together with physically motivated boundary conditions, uniquely fix the answer. All the cases considered give rise to uniform weight functions. Our most interesting example is a five-point non-planar hexa-box integral with an off-shell leg. It gives first indications on the function space needed for Higgs plus two jets production at next-to-next-to leading order.

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This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

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Affiliations

  1. Max-Planck-Institut für Physik, Werner-Heisenberg-Institut, 80805, München, Germany

    D. Chicherin & J. M. Henn

  2. LAPTh, Université Savoie Mont Blanc, CNRS, B.P. 110, F-74941, Annecy-le-Vieux, France

    E. Sokatchev

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  1. D. Chicherin
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  2. J. M. Henn
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Correspondence to D. Chicherin.

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ArXiv ePrint: 1811.02560

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Chicherin, D., Henn, J.M. & Sokatchev, E. Amplitudes from anomalous superconformal symmetry. J. High Energ. Phys. 2019, 179 (2019). https://doi.org/10.1007/JHEP01(2019)179

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Keywords

  • Scattering Amplitudes
  • Anomalies in Field and String Theories
  • Conformal Field Theory
  • Superspaces