All tree-level amplitudes in = 4 SYM

By J. Drummond, J. Henn. 2008

229 citations recorded by the source corpus.

We give an explicit formula for all tree amplitudes in = 4 SYM, derived by solving the recently presented supersymmetric tree-level recursion relations. The result is given in a compact, manifestly supersymmetric form and we show how to extract from it all possible component amplitudes for an arbitrary number of external particles and any arrangement of external particles and helicities. We focus particularly on extracting gluon amplitudes which are valid for any gauge theory. The formula for all tree-level amplitudes is given in terms of nested sums of dual superconformal invariants and it therefore manifestly respects both conventional and dual superconformal symmetry.

Subfields: Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/fffa24b548c2b52011587153a4fc9834933d52b6

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In Nuclear and High Energy Physics

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

Citations in the corpus

• Unification of residues and Grassmannian dualities (2009, background): “[16])—and therefore they become sums of residues of Ln,k.”
• Symmetries of Tree-level Scattering Amplitudes in N = 6 Superconformal Chern{Simons Theory (2010, background): “In addition to the standard superconformal symmetry, the dual realization acts on dual momentum variables leaving all N = 4 SYM tree-level amplitudes invariant [16].”
• Eliminating spurious poles from gauge-theoretic amplitudes (2009, background): “Note that Drummond and Henn (2008), in giving an explicit statement of all tree amplitudes, in a form which shows their dual conformal symmetry, still present the summation of many terms with spurious poles, and with all the hidden identities.”
• A brief introduction to modern amplitude methods (2013, unknown): “A closely related set of recursion relations for N = 4 super-Yang-Mills theory [27] have been solved in closed form for an arbitrary number of external legs [28].”
• Dual superconformal invariance, momentum twistors and Grassmannians (2009, methodology): “enominator acting as a Jacobian to compensate for the cyclic shift of the fermionic -functions in the numerator. We have checked for n7 that (116) agrees with the momentum space expression given in [7]. 5 Polytopes The dual superconformal invariants relevant for NMHV tree amplitudes have been previo”
• The all-loop integrand for scattering amplitudes in planar $ \mathcal{N} = 4 $ SYM (2010, background): “. Further investigations [44] identied a new principle, the Grassmannian \particle interpretation", which determines the correct contour of integration yielding the BCFW form of tree amplitudes [45]. Quite remarkably, a deformation of the integrand connects this formulation to twistor string th”
• Color-kinematics duality for QCD amplitudes (2015, background): “Such primitive amplitudes are gauge-invariant and are often computed via off-shell [27] or on-shell recursion [6, 7], which admits an analytic all-multiplicity solution [28, 29] for massless QCD with up to four quark-antiquark pairs.”
• Scattering Amplitudes and the Positive Grassmannian (2012, background): “[10, 70, 71, 148, 150]), its extension to all-loop integrands remains relatively novel—and until now, has only been understood in terms of momentum-twistor variables (as described in [13]).”