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MHV diagrams in momentum twistor space

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Abstract

We show that there are remarkable simplifications when the MHV diagram formalism for \( \mathcal{N} = 4 \) super Yang-Mills is reformulated in momentum twistor space. The vertices are replaced by unity while each propagator becomes a dual superconformal ‘R-invariant’ whose arguments may be read off from the diagram, and include an arbitrarily chosen reference twistor. The momentum twistor MHV rules generate a formula for the full, all-loop planar integrand for the super Yang-Mills S-matrix that is manifestly dual superconformally invariant up to the choice of a reference twistor. We give a general proof of this reformulation and illustrate its use by computing the momentum twistor NMHV and N2MHV tree amplitudes and the integrands of the MHV and NMHV 1-loop and the MHV 2-loop planar amplitudes.

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Authors and Affiliations

  1. Rudolf Peierls Centre for Theoretical Physics, 1 Keble Road, Oxford, OX1 3NP, United Kingdom

    Mathew Bullimore

  2. The Mathematical Institute, 24-29 St. Giles’, Oxford, OX1 3LB, United Kingdom

    Lionel Mason

  3. Perimeter Institute for Theoretical Physics, 31 Caroline St., Waterloo, ON, N2L 2Y5, Canada

    David Skinner

Authors
  1. Mathew Bullimore
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  2. Lionel Mason
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  3. David Skinner
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Correspondence to David Skinner.

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Bullimore, M., Mason, L. & Skinner, D. MHV diagrams in momentum twistor space. J. High Energ. Phys. 2010, 32 (2010). https://doi.org/10.1007/JHEP12(2010)032

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