Nonsinglet pentagons and NMHV amplitudes

TL;DR

The paper develops a nonperturbative framework for twist-two contributions to NMHV amplitudes in ${\mathcal N}=4$ SYM by refining the OPE of the null polygonal super Wilson loop into pentagon transitions in the flux-tube picture. It derives flux-tube equations from the spin-chain Baxter formalism, constructs complete (mirror-covariant) S-matrices for all main flux-tube excitations, and proposes axioms for nonsinglet pentagon form factors that are solved to all orders in the 't Hooft coupling. The nonsinglet two-particle states—primarily hole-gluon and two-fermion composites—are shown to reproduce NMHV twist-two contributions, with explicit perturbative checks up to four loops and clear predictions for higher orders. The work clarifies the role of small- versus large-fermion sheets and the necessity of nonsinglet pentagons to access Grassmann components of NMHV amplitudes, thereby advancing a fully nonperturbative, integrability-based route to scattering amplitudes in maximally supersymmetric gauge theory.

Abstract

Scattering amplitudes in maximally supersymmetric gauge theory receive a dual description in terms of the expectation value of the super Wilson loop stretched on a null polygonal contour. This makes the analysis amenable to nonperturbative techniques. Presently, we elaborate on a refined form of the operator product expansion in terms of pentagon transitions to compute twist-two contributions to NMHV amplitudes. To start with, we provide a novel derivation of scattering matrices starting from Baxter equations for flux-tube excitations propagating on magnon background. We propose bootstrap equations obeyed by pentagon form factors with nonsinglet quantum numbers with respected to the R-symmetry group and provide solutions to them to all orders in 't Hooft coupling. These are then successfully confronted against available perturbative calculations for NMHV amplitudes to three-loop order.

Figures (5)

• Figure 1: Hexagon Wilson loop decomposition into pentagon transitions.
• Figure 2: Relation between $F_{\rm hg}$ and $F_{\rm gh}$ form factors through a mirror transformation that brings the excitation in a complete cycle around the contour (left panel). A particular way to obtain the pentagon transition $P_{\rm hg}$ as a double mirror transformation in hole rapidity of the hole-gluon form factor (right panel).
• Figure 3: The path (in green) of analytic continuation from large to small fermion. In blue, we display the integration contour $C = C_{\rm F} \cup C_{\rm f}$ for integrals in Eq. (\ref{['W2fermion']}).
• Figure 4: The path of analytic continuation to the mirror kinematics for scalars.
• Figure 5: The path of analytic continuation to the mirror kinematics for gluons. For simplicity, the real and mirror sheets are shown to coincide here. They do not.