Abstract
We investigate the Yangian symmetry of scattering amplitudes in N=4 super Yang-Mills theory and show that its formulations in twistor and momentum twistor space can be interchanged. In particular we show that the full symmetry can be thought of as the Yangian of the dual superconformal algebra, annihilating the amplitude with the MHV part factored out. The equivalence of this picture with the one where the ordinary superconformal symmetry is thought of as fundamental is an algebraic expression of T-duality. Motivated by this, we analyse some recently proposed formulas, which reproduce different contributions to amplitudes through a Grassmannian integral. We prove their Yangian invariance by directly applying the generators.
Highlights
We investigate the Yangian symmetry of scattering amplitudes in N = 4 super Yang-Mills theory and show that its formulations in twistor and momentum twistor space can be interchanged
In particular we show that the full symmetry can be thought of as the Yangian of the dual superconformal algebra, annihilating the amplitude with the MHV part factored out
The breaking of the original superconformal symmetry by loop corrections is still not completely understood, while the breaking of the dual conformal symmetry is under control and it is identified with the breaking of the conformal symmetry of the Wilson loop in the dual space
Summary
When we consider scattering amplitudes of the on-shell superfields we have that the helicity condition (or ‘homogeneity condition’) is satisfied for each particle, i.e. hiA(Φ1, . The tree-level amplitudes in N = 4 super Yang-Mills theory can be written as follows, A(Φ1, . The tree-level amplitude is necessarily a particular linear combination of the one-loop box function coefficients due to consistency with the condition of infrared factorisation [42]. Other coefficients at one-loop, the four-mass box coefficients, do not appear at tree-level as the corresponding integrals are infrared finite. The one-loop coefficients cI can be determined by comparing the discontinuities of the amplitude with those of the scalar box integrals [41, 43, 44]. The coefficients can be determined again by comparing the discontinuities of the amplitude and the integrals
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