Solving Scattering in N=4 Super-Yang-Mills Theory

TL;DR

This paper reviews ongoing research into the structure of scattering amplitudes in planar N=4 super-Yang-Mills theory, highlighting its significance in high-energy physics and mathematical physics.

Contribution

It summarizes recent advances and the importance of N=4 super-Yang-Mills theory in understanding scattering amplitudes and related mathematical structures.

Findings

Planar N=4 super-Yang-Mills theory is exactly solvable in four dimensions.

It serves as a model for developing new computational methods.

The theory provides insights into geometrical formulations of quantum field theory.

Abstract

As part of the Snowmass community planning exercise, we highlight an ongoing program of research into the structure of scattering amplitudes in N=4 super-Yang-Mills theory, particularly in the planar limit of a large number of colors. This theory sits at the nexus of a number of exciting topics in high-energy particle physics, including the AdS/CFT correspondence, conformal field theory, integrability, and string theory, and is believed to be exactly solvable in four dimensions. In many ways, planar N=4 super-Yang-Mills theory is the "hydrogen atom" of relativistic scattering: It has proven indispensable for learning about new geometrical formulations of quantum field theory, for exploring mathematical properties at high perturbative orders, and for developing powerful new computational methods that have found applicability in precision collider physics.