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The Amplituhedron

Journal of High Energy Physics volume 2014, Article number: 30 (2014) Cite this article

A preprint version of the article is available at arXiv.

Abstract

Perturbative scattering amplitudes in gauge theories have remarkable simplicity and hidden infinite dimensional symmetries that are completely obscured in the conventional formulation of field theory using Feynman diagrams. This suggests the existence of a new understanding for scattering amplitudes where locality and unitarity do not play a central role but are derived consequences from a different starting point. In this note we provide such an understanding for \( \mathcal{N}=4 \) SYM scattering amplitudes in the planar limit, which we identify as “the volume” of a new mathematical object — the Amplituhedron — generalizing the positive Grassmannian. Locality and unitarity emerge hand-in-hand from positive geometry.

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  1. School of Natural Sciences, Institute for Advanced Study, 1 Einstein Dr., Princeton, NJ, 08540, United Kingdom

    Nima Arkani-Hamed

  2. Walter Burke Institute for Theoretical Physics, California Institute of Technology, 1200 E Colorado Blvd., Pasadena, CA, 91125, United Kingdom

    Jaroslav Trnka

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  1. Nima Arkani-Hamed
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  2. Jaroslav Trnka
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Correspondence to Jaroslav Trnka.

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ArXiv ePrint: 1312.2007

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Arkani-Hamed, N., Trnka, J. The Amplituhedron. J. High Energ. Phys. 2014, 30 (2014). https://doi.org/10.1007/JHEP10(2014)030

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Keywords

  • Supersymmetric gauge theory
  • Scattering Amplitudes