Lectures on the Infrared Structure of Gravity and Gauge Theory

TL;DR

The work outlines a unifying infrared framework for gauge theories and gravity, linking soft theorems, asymptotic symmetries, and memory effects into an interconnected triangle. It develops explicit canonical and diagrammatic derivations of soft theorems in QED and gravity, reveals infinite-dimensional asymptotic symmetry algebras (including BMS and its extensions), and demonstrates how memory effects realize symmetry actions in physical data. The lectures extend these ideas to nonabelian theories, supersymmetry, massive states, and magnetic charges, and connect the S-matrix to celestial CFT structures, with profound implications for flat-space holography and black-hole information via soft hair. The material culminates in applications to black hole physics, the information paradox, and horizon dynamics, emphasizing that IR degrees of freedom encode rich information about spacetime and quantum states. Overall, the IR triangle provides a powerful, far-reaching framework for understanding long-distance physics in massless gauge and gravitational theories and suggests new avenues toward a holographic description of flat-space quantum gravity.

Abstract

This is a redacted transcript of a course given by the author at Harvard in spring semester 2016. It contains a pedagogical overview of recent developments connecting the subjects of soft theorems, the memory effect and asymptotic symmetries in four-dimensional QED, nonabelian gauge theory and gravity with applications to black holes. The lectures may be viewed online at https://goo.gl/3DJdOr. Please send typos or corrections to strominger@physics.harvard.edu.

Figures (23)

• Figure 1: The infrared triangle.
• Figure 2: The infrared triangle echoes throughout disparate areas of physics.
• Figure 3: Penrose diagram of Minkowski space. Red lines represent surfaces of constant $t$, while blue lines represent surfaces of constant $r$. The thick gray line is the worldline of a massive particle moving at constant velocity, and the thick wavy gray line is a light ray. Every two-sphere of constant $(r>0,t)$ is represented by two points, one on the left and one on the right, which are exchanged by the antipodal map. Past and future null infinities are labelled by ${\mathcal{I}}^\pm$, and their four $S^2$ boundary components by ${\mathcal{I}}^\pm_\pm$. The points $i^\pm$ are past and future timelike infinity, while the point $i^0$ is spatial infinity.
• Figure 4: Alternative Penrose diagram of Minkowski space in which every point except for $r=0$ is an $S^2$.
• Figure 5: The blue diamond represents Minkowski space conformally compactified onto the $S^3\times \mathbb{R}$ Einstein static universe. The red arrows indicate how the generators of null infinity pass through spatial infinity.