An Origin Story for Amplitudes

TL;DR

This paper classifies the origin limits of multi-gluon scattering amplitudes in planar N=4 super-Yang-Mills theory using cluster algebras, providing conjectures for exact expressions involving the cusp anomalous dimension.

Contribution

It introduces a classification of amplitude limits via cluster algebras and proposes exact formulas for amplitudes with up to 8 gluons based on strong coupling data.

Findings

Amplitudes become exponential of quadratic polynomials in large logs.

Evidence supports the conjecture of exact amplitude expressions.

Expressions involve the tilted cusp anomalous dimension at various angles.

Abstract

We classify origin limits of maximally helicity violating multi-gluon scattering amplitudes in planar $\mathcal{N}=4$ 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 8 gluons in all origin limits. Our expressions are governed by the tilted cusp anomalous dimension evaluated at various values of the tilt angle.