All-Orders Quadratic-Logarithmic Behavior for Amplitudes

We classify origin limits of maximally helicity violating multigluon scattering amplitudes in planar N = 4 super-Yang-Mills theory, where a large number of cross ratios approach zero, with the help of cluster algebras. By analyzing existing perturbative data and bootstrapping new data, we provide evidence that the amplitudes become the exponential of a quadratic polynomial in the large logarithms. With additional input from the thermodynamic Bethe ansatz at strong coupling, we conjecture exact expressions for amplitudes with up to eight gluons in all origin limits. Our expressions are governed by the tilted cusp anomalous dimension evaluated at various values of the tilt angle.

Automated summary

We use cluster algebras to classify the origin limits of maximally helicity violating multigluon scattering amplitudes in planar N = 4 super-Yang-Mills theory. By analyzing perturbative data and bootstrapping new data, we find evidence that the amplitudes become the exponential of a quadratic polynomial in the large logarithms. With input from the thermodynamic Bethe ansatz at strong coupling, we propose exact expressions for amplitudes with up to eight gluons in all origin limits, which are governed by the tilted cusp anomalous dimension evaluated at various tilt angles.