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All-Orders Quadratic-Logarithmic Behavior for Amplitudes.

Benjamin Basso1, Lance J Dixon2, Yu-Ting Liu2,3

  • 1Laboratoire de Physique de l'Ecole Normale Supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université Paris Cité, F-75005 Paris, France.

Physical Review Letters
|March 31, 2023
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Summary
This summary is machine-generated.

We classify scattering amplitudes in N=4 super-Yang-Mills theory using cluster algebras. Our findings suggest amplitudes are the exponential of a quadratic polynomial in large logarithms, with exact expressions conjectured for up to eight gluons.

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Area of Science:

  • High-energy physics
  • Quantum field theory
  • String theory

Background:

  • Maximally helicity violating (MHV) scattering amplitudes are crucial in understanding quantum field theories.
  • Planar N=4 super-Yang-Mills theory provides a tractable framework for studying non-perturbative phenomena.
  • Cluster algebras offer a novel algebraic structure relevant to scattering amplitudes.

Purpose of the Study:

  • To classify the origin limits of MHV multigluon scattering amplitudes in planar N=4 super-Yang-Mills theory.
  • To explore the behavior of these amplitudes as various cross ratios approach zero.
  • To develop exact expressions for these amplitudes using insights from cluster algebras and other theoretical tools.

Main Methods:

  • Utilizing cluster algebras to analyze the structure of scattering amplitudes.
  • Analyzing existing perturbative data and bootstrapping new data points.
  • Employing the thermodynamic Bethe ansatz (TBA) at strong coupling.
  • Investigating the role of the tilted cusp anomalous dimension.

Main Results:

  • Evidence is provided that the amplitudes take the form of an exponential of a quadratic polynomial in large logarithms.
  • Exact expressions for amplitudes with up to eight gluons in all origin limits are conjectured.
  • The behavior of the amplitudes is shown to be governed by the tilted cusp anomalous dimension.

Conclusions:

  • The study successfully classifies origin limits of scattering amplitudes in a key theoretical model.
  • The findings offer a new perspective on the structure of scattering amplitudes, connecting them to cluster algebras and anomalous dimensions.
  • The conjectured exact expressions provide testable predictions and avenues for future research in quantum field theory.