The complete planar S-matrix of $ \mathcal{N} = 4 $ SYM as a Wilson loop in twistor space
By L. Mason, David Skinner. 2010
200 citations recorded by the source corpus.
We show that the complete planar S-matrix of $ \mathcal{N} = 4 $ super Yang-Mills — including all NkMHV partial amplitudes to all loops — is equivalent to the correlation function of a supersymmetric Wilson loop in twistor space. Remarkably, the entire classical S-matrix arises from evaluating the correlation function in the self-dual sector, while the expansion of the correlation function in powers of the Yang-Mills coupling constant provides the loop expansion of the amplitudes. We support our proposal with explicit computations of the n particle NMHV and N2MHV trees, the integrands of the 1-loop MHV and NMHV amplitudes, and the n particle 2-loop MHV amplitude. These calculations are performed using the twistor action in axial gauge. In this gauge, the Feynman diagrams of the correlation function are the planar duals of the usual MHV diagrams for the scattering amplitude. The results are presented in the form of a sum of products of dual superconformal invariants in (momentum) twistor space, and agree with the expressions derived in the companion paper [1] directly from the MHV rules. The twistor space Wilson loop is a natural supersymmetric generalization of the standard Wilson loop used to compute MHV amplitudes. We show how the Penrose-Ward transform can be used to determine a corresponding supersymmetrization on space-time and give the corresponding superconnection in the abelian case.
Subfields: Nuclear and High Energy Physics
View Paper: https://www.semanticscholar.org/paper/5243228789397ed8b0466b9f4ece5ae8f6518d1d
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Nuclear and High Energy Physics
Citations in the corpus
- Bootstrapping an NMHV amplitude through three loops (2014, background): “In general, NMHV scattering amplitudes are dual to Wilson loops dressed with insertions of states that depend on the particular NMHV component being investigated [82, 83].”
- Local integrals for planar scattering amplitudes (2010, background): “3 4 5 6 × ([2 3 4 5 6]− [3 4 5 6 1] + [4 5 6 1 2]) , (4.”
- When does the gluon reggeize? (2013, background): “[120–123], which naturally led to its proof to all-order in perturbation theory (the amplitude and Wilson loops being both expressed as integrals over the same, recursively constructed, integrands).”
- A symbol of uniqueness: the cluster bootstrap for the 3-loop MHV heptagon (2014, background): “unction [42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53]. Finally, the extension of dual conformal symmetry to dual superconformal symmetry [54], is expressed via the super-Wilson-loop correspondence [55, 56, 57] in terms of recursive differential equations [58, 59] which imply certain universal cons”