Aspects of Symmetry in the Infrared

Abstract

This dissertation studies a class of infinite-dimensional symmetries, known as asymptotic symmetries, across a variety of gauge and gravitational theories. In identifying the physical implications of these symmetries with other well-known infrared phenomena, a precise equivalence is established among soft theorems, memory effects and asymptotic symmetries, called the infrared triangle. In U(1) gauge theories with only massless charged particles, the soft photon theorem was previously identified as the Ward identity of an infinite-dimensional asymptotic symmetry group. The symmetry group comprises of gauge transformations which approach angle-dependent constants at null infinity. Here, the analysis is extended to all U(1) theories, including those with massive charged particles such as QED. Next, implications of the U(1) large gauge symmetry for a holographic dual are considered. The soft factorization theorem for 4D abelian gauge theory is shown to be mathematically equivalent to the factorization of correlation functions on the sphere in a 2D CFT with a U(1) Kac-Moody current algebra. The soft ‘t Hooft-Wilson lines and soft photons are realized as a complexified 2D current algebra on the celestial sphere at null infinity with the level determined by the cusp anomalous dimension. Then, a universal gravitational memory effect, measurable by inertial detectors, is established in even spacetime dimensions d > 4. The effect exhibits (3-d)th power law fall-off behavior at large radius r and belongs to an infrared triangle that includes Weinberg’s soft graviton theorem and infinite-dimensional asymptotic symmetries. In the final part of this dissertation, color memory - the non-abelian gauge theoretic analog of the gravitational memory effect - is determined. A formula for the net relative SU(3) color rotation of a pair of nearby quarks that is induced by the transit of color radiation is derived from conservation laws for large gauge symmetry in non-abelian gauge theories. For weak color flux, it linearizes to the Fourier transform of the soft gluon theorem. It is proposed that this effect can be measured in the Regge limit of deeply inelastic scattering at electron-ion colliders.