OPE for Super Loops

TL;DR

The paper extends the OPE framework for supersymmetric Null Polygon Wilson loops to the Mason-Skinner-Caron-Huot super loop, enabling the promotion of tree-level NMHV data to all loop orders via flux-tube excitations and integrability. It shows how SUSY Ward identities allow bootstrap of all one-loop NMHV six-point amplitudes from tree-level expressions and provides all-loop predictions, highlighting a path to systematically access higher-loop NMHV data. The approach relies on decomposing amplitudes into SL(2) conformal blocks for flux-tube excitations and exploiting helicity weights, cross-ratio dynamics, and Ward identities to relate components across channels. The results validate known one-loop NMHV results and establish a scalable, symmetry-guided program for predicting higher-loop structure in planar N=4 SYM amplitudes.

Abstract

We extend the Operator Product Expansion for Null Polygon Wilson loops to the Mason-Skinner-Caron-Huot super loop, dual to non MHV gluon amplitudes. We explain how the known tree level amplitudes can be promoted into an infinite amount of data at any loop order in the OPE picture. As an application, we re-derive all one loop NMHV six gluon amplitudes by promoting their tree level expressions. We also present some new all loops predictions for these amplitudes.

Figures (5)

• Figure 1: The OPE picture. Flux tube excitations are created at the bottom and absorbed in the top. The flux is tick in spacetime but is 1+1 dimensional in AdS. Its excitations are integrable.
• Figure 2: One remarkable property of the Super Wilson Loop/Scattering Amplitude duality is that a N$^k$MHV scattering amplitude at $l$ loops is given, roughly, by a $k+l$ Wilson loop computation. This means that the known tree and one loop data from Scattering amplitude present an excellent window towards higher loop physics from the Wilson loop point of view. In particular, multi-particle flux tube excitations can in principle be studies with the already available data.
• Figure 3: $\eta_2\eta_3\eta_5\eta_6$ component at tree level (left) and at one loop level (right). At one loop there are three contributions that kick in as indicated in the figure. From the OPE point of view the interaction with the flux tube is under control since we can compute the energy of the flux tube excitations exactly using integrability Benjamin.
• Figure 4: Some components with a good OPE expansion in the channel defined by the null edges 1 and 4. The first two are given by scalars propagating from bottom to top and the third is described by propagation of fermions.
• Figure 5: Ward Identities allow us to relate any six point scattering amplitude to a base of five components. In particular this allows us to access the behavior of any amplitude in any OPE channel. In the figure the component $\eta_1\eta_1\eta_4\eta_4$, which clearly does not have a natural expansion in the channel defined by the null edges 1 and 4 is expanded in terms of five components that do admit a neat expansion in this channel. This can be done at any loop order. Ward identities replace channel duality in this problem.