Journal of High Energy Physics

, 2011:116 | Cite as

On all-loop integrands of scattering amplitudes in planar \( \mathcal{N} = 4 \) SYM

  • Song He
  • Tristan McLoughlinEmail author


We study the relationship between the momentum twistor MHV vertex expansion of planar amplitudes in \( \mathcal{N} = 4 \) super-Yang–Mills and the all-loop generalization of the BCFW recursion relations. We demonstrate explicitly in several examples that the MHV vertex expressions for tree-level amplitudes and loop integrands satisfy the recursion relations. Furthermore, we introduce a rewriting of the MHV expansion in terms of sums over non-crossing partitions and show that this cyclically invariant formula satisfies the recursion relations for all numbers of legs and all loop orders.


Supersymmetric gauge theory AdS-CFT Correspondence Integrable Field Theories 


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Copyright information

© SISSA, Trieste, Italy 2011

Authors and Affiliations

  1. 1.Max-Planck-Institut für GravitationsphysikAlbert-Einstein-InstitutPotsdamGermany

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