A Note on dual superconformal symmetry of the N=4 super Yang-Mills S-matrix

By A. Brandhuber, P. Heslop, G. Travaglini. 2008

296 citations recorded by the source corpus.

We present a supersymmetric recursion relation for tree-level scattering amplitudes in N=4 super Yang-Mills. Using this recursion relation, we prove that the tree-level S matrix of the maximally supersymmetric theory is covariant under dual superconformal transformations. We further analyze the consequences that the transformation properties of the trees under this symmetry have on those of the loops. In particular, we show that the coefficients of the expansion of generic one-loop amplitudes in a basis of pseudoconformally invariant scalar box functions transform covariantly under dual superconformal symmetry, and in exactly the same way as the corresponding tree-level amplitudes.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/eaf2b243fc1d7085f4116d7c78ac43e45e5a8d54

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In Astronomy and Astrophysics

1. C. Cheung
2. N. Arkani-Hamed
3. L. Dixon
4. J. Drummond
5. L. Mason
6. Yu-tin Huang
7. F. Cachazo
8. David Skinner

In Nuclear and High Energy Physics

1. N. Arkani-Hamed
2. S. Caron-Huot
3. L. Dixon
4. C. Cheung
5. F. Cachazo
6. J. Trnka
7. L. Mason
8. J. Drummond

Citations in the corpus

• TASI Lectures on Scattering Amplitudes (2017, background): “On-shell tools have excavated a landscape of structures: hidden Yangian and dual conformal symmetries [80, 81, 82, 83, 84], reformulations of the S-matrix in twistor space [85, 86, 22, 87, 88, 89, 90, 91] and Grassmannian space [92, 93, 94], as well as connections to abstract volumes [12, 95] like t”
• The all-loop integrand for scattering amplitudes in planar $ \mathcal{N} = 4 $ SYM (2010, methodology): “5 The BCFW Bridge A particularly important way of putting together two Yangian invariants to make a third is the “BCFW bridge” [7,70,71], associated with the familiar “two-mass hard” leading singularities drawn below in twistor space [70–73]:”
• Notes on the scattering amplitude — Wilson loop duality (2010, unknown): “also [20] for the supersymmetric version).”
• Loop corrections to soft theorems in gauge theories and gravity (2014, methodology): “Similarly one can study N = 4 SYM by applying supersymmetric BCFW recursion relation [38, 39], where the leading divergent part is still controlled by the BCFW diagram figure 1 (again with i = 1).”
• Dual superconformal invariance, momentum twistors and Grassmannians (2009, background): “The MHV and six particle NMHV tree amplitudes were shown to be covariant under dual superconformal transformations in [1] (the MHV prefactor having weight under dual special conformal transformations) and this was generalised to all tree amplitudes in [5].”
• Superconformal symmetry and two-loop amplitudes in planar N = 4 super Yang-Mills (2011, background): “These leading singularities have been proved to be Yangian invariant [23, 44].”
• Yangian symmetry of scattering amplitudes in N=4 super Yang-Mills theory (2009, methodology): “For tree-level amplitudes, dual superconformal symmetry was verified recursively [42] by employing a supersymmetrised version [42–44] of the BCFW recursion relations [15, 16].”
• Scattering amplitudes and Wilson loops in twistor space (2011, methodology): “As well as being superconformally invariant, the BCFW procedure was also shown to be dual superconformally invariant in [99] where it was used to prove dual superconformal invariance of all tree amplitudes.”