Gauge and Gravity Amplitude Relations

TL;DR

This paper discusses recent discoveries of universal structures and simplifications in gauge and gravity scattering amplitudes, emphasizing graphical principles like color-kinematics duality and double-copy relations for multi-loop calculations.

Contribution

It introduces graphical organizational principles that reveal new relationships in gauge and gravity amplitudes, with examples from maximally supersymmetric theories and applications to multi-loop integrand construction.

Findings

Identification of gauge-theoretic color-kinematics duality

Explanation of gravitational double-copy structure

Application to multi-loop scattering amplitude calculations

Abstract

In these lectures I talk about simplifications and universalities found in scattering amplitudes for gauge and gravity theories. In contrast to Ward identities, which are understood to arise from familiar symmetries of the classical action, these structures are currently only understood in terms of graphical organizational principles, such as the gauge-theoretic color-kinematics duality and the gravitational double-copy structure, for local representations of multi-loop S-matrix elements. These graphical principles make manifest new relationships in and between gauge and gravity scattering amplitudes. My lectures will focus on arriving at such graphical organizations for generic theories with examples presented from maximal supersymmetry, and their use in unitarity-based multi-loop integrand construction.