Abstract
Abstract We extend the Operator Product Expansion (OPE) for scattering amplitudes in planar $$ \mathcal{N}=4 $$ N = 4 SYM to account for all possible helicities of the external states. This is done by constructing a simple map between helicity configurations and so-called charged pentagon transitions. These OPE building blocks are generalizations of the bosonic pentagons entering MHV amplitudes and they can be bootstrapped at finite coupling from the integrable dynamics of the color flux tube. A byproduct of our map is a simple realization of parity in the super Wilson loop picture.
Highlights
In the dual Wilson loop picture, NkMHV amplitudes are computed by a super Wilson loop decorated by adjoint fields inserted on the edges and cusps [15, 16]
In this paper we have constructed a simple map between NkMHV amplitudes and socalled charged pentagon transitions
In the dual super-loop description of the amplitude, the charged transitions are operators that act on the color flux tube
Summary
In the dual Wilson loop picture, NkMHV amplitudes are computed by a super Wilson loop decorated by adjoint fields inserted on the edges and cusps [15, 16]. (We can understand this as coming from the three possible irreducible representations in 6 ⊗ 6 or, equivalently, as the three inequivalent ways of forming singlets in 6⊗6⊗6⊗6.) to count the number of N2MHV charged polygons we have to consider the number of ways of distributing eight units of charge within four pentagons and to weight that counting by the number of inequivalent contractions of all the R-charge indices. This counting is identical to the one found in [19] based on analysis of the SUSY Ward identities. The step is to endow the charged pentagon construction with a precise dictionary between charged polygons and helicity configurations of scattering amplitudes
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